IBEW: Electrical Training Alliance Aptitude Test Quiz: Simplify Polynomials
20 questions · exam conditions
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Simplify PolynomialsQuestion 1 of 20

Simplify the expression: 5a−2b+8−3a+5b−25a - 2b + 8 - 3a + 5b - 2

2a+3b+102a + 3b + 10
2a−7b+62a - 7b + 6
2a+3b+62a + 3b + 6
8a+7b+108a + 7b + 10
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IBEW: Electrical Training Alliance Aptitude Test Quiz

IBEW: Electrical Training Alliance Aptitude Test Quiz: Simplify Polynomials

Practice Simplify Polynomials in IBEW: Electrical Training Alliance Aptitude Test with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Simplify Polynomials, giving you a quick way to practice the rules, question types, and explanations that matter most for IBEW: Electrical Training Alliance Aptitude Test.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Simplify the expression: 5a−2b+8−3a+5b−25a - 2b + 8 - 3a + 5b - 2

  1. 2a+3b+102a + 3b + 10
  2. 2a−7b+62a - 7b + 6
  3. 2a+3b+62a + 3b + 6 (correct answer)
  4. 8a+7b+108a + 7b + 10
Explanation: This question tests your ability to simplify algebraic expressions by combining like terms—a fundamental skill you'll use throughout electrical calculations involving variables and formulas. To simplify 5a−2b+8−3a+5b−25a - 2b + 8 - 3a + 5b - 2, you need to group and combine terms with the same variables. Start by rearranging to group like terms together: (5a−3a)+(−2b+5b)+(8−2)(5a - 3a) + (-2b + 5b) + (8 - 2). Now combine each group:
  • For the aa terms: 5a−3a=2a5a - 3a = 2a
  • For the bb terms: −2b+5b=3b-2b + 5b = 3b
  • For the constants: 8−2=68 - 2 = 6
This gives you 2a+3b+62a + 3b + 6, which matches answer choice C. Let's examine why the other options are incorrect. Choice A gives 2a+3b+102a + 3b + 10—this correctly combines the variable terms but incorrectly adds the constants as 8+2=108 + 2 = 10 instead of 8−2=68 - 2 = 6. Choice B shows 2a−7b+62a - 7b + 6—while the aa terms and constants are correct, the bb terms were incorrectly calculated as −2b−5b=−7b-2b - 5b = -7b instead of −2b+5b=3b-2b + 5b = 3b. Choice D presents 8a+7b+108a + 7b + 10—this contains multiple errors, treating subtraction as addition throughout. When simplifying algebraic expressions, always pay careful attention to positive and negative signs. Write out each step clearly and double-check your arithmetic. These skills are essential for solving electrical formulas involving resistance, voltage, and current calculations on the IBEW exam.

Question 2

Simplify the expression: 12+5z−9+8w−3z+2w12 + 5z - 9 + 8w - 3z + 2w

  1. 3+2z+10w3 + 2z + 10w (correct answer)
  2. 3+8z+6w3 + 8z + 6w
  3. −3+2z+10w-3 + 2z + 10w
  4. 21+8z+10w21 + 8z + 10w
Explanation: This question tests your ability to combine like terms in an algebraic expression, a fundamental skill you'll use throughout electrical calculations involving variables like voltage, current, and resistance. To simplify 12+5z−9+8w−3z+2w12 + 5z - 9 + 8w - 3z + 2w, you need to group and combine terms with the same variables. Start by identifying three types of terms: constants (numbers without variables), terms with zz, and terms with ww. Constants: 12−9=312 - 9 = 3 Terms with zz: 5z−3z=2z5z - 3z = 2z
Terms with ww: 8w+2w=10w8w + 2w = 10w Combining these results gives you 3+2z+10w3 + 2z + 10w, which matches choice A. Let's examine why the other options are incorrect. Choice B (3+8z+6w3 + 8z + 6w) correctly finds the constant term but makes errors with the variables—it adds 5z+3z=8z5z + 3z = 8z instead of 5z−3z=2z5z - 3z = 2z, and calculates 8w−2w=6w8w - 2w = 6w instead of 8w+2w=10w8w + 2w = 10w. Choice C (−3+2z+10w-3 + 2z + 10w) handles the variable terms correctly but miscalculates the constants as 12−9=−312 - 9 = -3 instead of 33. Choice D (21+8z+10w21 + 8z + 10w) adds all constants together regardless of their signs (12+9=2112 + 9 = 21) and makes the same zz-term error as choice B. When combining like terms, always pay careful attention to the signs in front of each term. A minus sign applies to the entire term that follows it, not just the coefficient.

Question 3

Simplify the following expression by combining like terms: 7x+4y−3x+2y7x + 4y - 3x + 2y

  1. 4x+6y4x + 6y (correct answer)
  2. 4x+2y4x + 2y
  3. 10x+6y10x + 6y
  4. 10xy10xy
Explanation: When you encounter algebraic expressions with multiple terms, your goal is to identify and combine like terms—terms that have identical variable parts. This is a fundamental skill you'll use constantly in electrical calculations involving formulas and equations. To solve 7x+4y−3x+2y7x + 4y - 3x + 2y, group the like terms together. The xx terms are 7x7x and −3x-3x, while the yy terms are 4y4y and 2y2y. Combine each group separately: 7x−3x=4x7x - 3x = 4x and 4y+2y=6y4y + 2y = 6y. This gives you 4x+6y4x + 6y. Looking at the answer choices: Choice A (4x+6y4x + 6y) correctly combines the like terms as shown above. Choice B (4x+2y4x + 2y) correctly handles the xx terms but fails to add the yy terms—it keeps only the first yy term instead of combining 4y+2y=6y4y + 2y = 6y. Choice C (10x+6y10x + 6y) correctly combines the yy terms but incorrectly adds the xx terms—it treats the subtraction as addition, calculating 7x+3x=10x7x + 3x = 10x instead of 7x−3x=4x7x - 3x = 4x. Choice D (10xy10xy) represents a fundamental misunderstanding, incorrectly multiplying unlike terms together instead of keeping them separate. Remember this pattern: you can only combine terms with identical variable parts. Terms like 7x7x and 3x3x can combine, but xx and yy terms must remain separate. Always pay careful attention to signs—especially negative signs that indicate subtraction rather than addition.

Question 4

Simplify the following expression: 15j−8k+7−(5j−3k+2)15j - 8k + 7 - (5j - 3k + 2)

  1. 10j−11k+910j - 11k + 9
  2. 10j−5k+510j - 5k + 5 (correct answer)
  3. 10j−5k+910j - 5k + 9
  4. 20j−11k+520j - 11k + 5
Explanation: This question tests your ability to distribute negative signs and combine like terms—fundamental algebraic skills you'll use regularly in electrical calculations involving complex numbers and circuit analysis. To solve 15j−8k+7−(5j−3k+2)15j - 8k + 7 - (5j - 3k + 2), you must first distribute the negative sign to every term inside the parentheses. The expression becomes: 15j−8k+7−5j+3k−215j - 8k + 7 - 5j + 3k - 2. Notice that −(5j−3k+2)-(5j - 3k + 2) becomes −5j+3k−2-5j + 3k - 2. Now combine like terms by grouping similar variables and constants:
  • jj terms: 15j−5j=10j15j - 5j = 10j
  • kk terms: −8k+3k=−5k-8k + 3k = -5k
  • Constants: 7−2=57 - 2 = 5
The simplified expression is 10j−5k+510j - 5k + 5, which matches answer B. Let's examine why the other answers are incorrect. Answer A (10j−11k+910j - 11k + 9) results from failing to distribute the negative sign properly—treating −(−3k)-(- 3k) as −3k-3k instead of +3k+3k, and incorrectly handling the constant term. Answer C (10j−5k+910j - 5k + 9) gets the variable terms right but adds the constants incorrectly (7+2=97 + 2 = 9 instead of 7−2=57 - 2 = 5). Answer D (20j−11k+520j - 11k + 5) comes from adding instead of subtracting the jj terms (15j+5j15j + 5j) and mishandling the kk terms. Remember: when distributing a negative sign, every term inside the parentheses changes sign. This is a common source of errors, so always double-check your distribution step before combining like terms.

Question 5

Simplify the expression: 9r−[3s+2(r−s)]9r - [3s + 2(r - s)]

  1. 7r−s7r - s (correct answer)
  2. 7r+s7r + s
  3. 7r−5s7r - 5s
  4. 11r+s11r + s
Explanation: When you encounter algebraic expressions with brackets and parentheses, you must work systematically from the inside out, following the order of operations. This type of simplification problem tests your ability to distribute terms correctly and combine like terms. Let's work through 9r−[3s+2(r−s)]9r - [3s + 2(r - s)] step by step. First, handle the innermost parentheses by distributing the 2: 2(r−s)=2r−2s2(r - s) = 2r - 2s. Now the expression becomes: 9r−[3s+2r−2s]9r - [3s + 2r - 2s]. Next, simplify inside the brackets by combining like terms: 3s−2s=s3s - 2s = s, so we have 9r−[s+2r]9r - [s + 2r] or 9r−[2r+s]9r - [2r + s]. Finally, distribute the negative sign across the brackets: 9r−2r−s=7r−s9r - 2r - s = 7r - s. This matches answer choice A. Let's examine why the other options are incorrect. Answer B (7r+s7r + s) results from failing to distribute the negative sign properly — you'd get this if you wrote 9r−2r+s9r - 2r + s instead of 9r−2r−s9r - 2r - s. Answer C (7r−5s7r - 5s) comes from incorrectly combining the s terms, perhaps adding 3s+2s3s + 2s instead of 3s−2s3s - 2s. Answer D (11r+s11r + s) results from multiple errors: adding 9r+2r9r + 2r and failing to distribute the negative sign. Study tip: Always work inside-out with nested grouping symbols, and be extra careful with negative signs when distributing. Double-check your work by substituting simple values for the variables.

Question 6

What is the result of simplifying 1.5R+2.3S−0.7R+1.2S1.5R + 2.3S - 0.7R + 1.2S?

  1. 0.8R+3.5S0.8R + 3.5S (correct answer)
  2. 0.8R+1.1S0.8R + 1.1S
  3. 2.2R+3.5S2.2R + 3.5S
  4. 2.2R+1.1S2.2R + 1.1S
Explanation: When you encounter algebraic expressions with multiple terms, you need to combine like terms—terms that have the same variable. This is a fundamental skill you'll use constantly in electrical calculations involving resistance, current, and voltage relationships. To simplify 1.5R+2.3S−0.7R+1.2S1.5R + 2.3S - 0.7R + 1.2S, group the terms with the same variables together. First, collect all the R terms: 1.5R−0.7R1.5R - 0.7R. When subtracting, you get 1.5−0.7=0.81.5 - 0.7 = 0.8, so this becomes 0.8R0.8R. Next, collect all the S terms: 2.3S+1.2S2.3S + 1.2S. Adding these coefficients gives you 2.3+1.2=3.52.3 + 1.2 = 3.5, so this becomes 3.5S3.5S. The final simplified expression is 0.8R+3.5S0.8R + 3.5S. Looking at the wrong answers: Choice B (0.8R+1.1S0.8R + 1.1S) correctly finds the R coefficient but incorrectly subtracts the S terms instead of adding them (2.3−1.2=1.12.3 - 1.2 = 1.1). Choice C (2.2R+3.5S2.2R + 3.5S) correctly finds the S coefficient but adds the R terms instead of subtracting (1.5+0.7=2.21.5 + 0.7 = 2.2). Choice D (2.2R+1.1S2.2R + 1.1S) makes both mistakes—adding the R terms and subtracting the S terms. The correct answer is A: 0.8R+3.5S0.8R + 3.5S. Remember to pay careful attention to positive and negative signs when combining like terms. A systematic approach is to rewrite the expression grouping like terms together before performing the arithmetic—this reduces sign errors that commonly appear on the IBEW exam.

Question 7

Simplify the polynomial: 10−3v+4w−v−5w−210 - 3v + 4w - v - 5w - 2

  1. 12−4v+9w12 - 4v + 9w
  2. 8−4v−w8 - 4v - w (correct answer)
  3. 8−2v−w8 - 2v - w
  4. 8−4v+w8 - 4v + w
Explanation: When you encounter polynomial simplification problems, you're combining like terms—terms that have the same variable with the same exponent. The key is to group similar terms together and perform the arithmetic carefully. To simplify 10−3v+4w−v−5w−210 - 3v + 4w - v - 5w - 2, start by identifying and grouping like terms:
  • Constant terms: 1010 and −2-2
  • Terms with vv: −3v-3v and −v-v
  • Terms with ww: 4w4w and −5w-5w
Now combine each group:
  • Constants: 10+(−2)=810 + (-2) = 8
  • vv terms: −3v+(−v)=−3v−1v=−4v-3v + (-v) = -3v - 1v = -4v
  • ww terms: 4w+(−5w)=4w−5w=−w4w + (-5w) = 4w - 5w = -w
This gives you 8−4v−w8 - 4v - w, which matches answer choice B. Let's examine why the other answers are incorrect: Answer A (12−4v+9w12 - 4v + 9w) incorrectly adds the constants as 10+2=1210 + 2 = 12 instead of 10−2=810 - 2 = 8, and adds the ww terms as 4+5=94 + 5 = 9 instead of 4−5=−14 - 5 = -1. Answer C (8−2v−w8 - 2v - w) correctly handles the constants and ww terms but miscalculates the vv terms as −2v-2v instead of −4v-4v. Answer D (8−4v+w8 - 4v + w) gets the constants and vv terms right but shows +w+w instead of −w-w. Study tip: Always write out your work when combining like terms, and double-check your signs. Many errors come from rushing through the arithmetic or mishandling negative signs.

Question 8

Simplify the polynomial: ab−bc+ac−3ab+2bcab - bc + ac - 3ab + 2bc

  1. −2ab+3bc+ac-2ab + 3bc + ac
  2. −2ab−bc+ac-2ab - bc + ac
  3. −2ab+bc+ac-2ab + bc + ac (correct answer)
  4. −3ab+2bc+ac-3ab + 2bc + ac
Explanation: When you encounter polynomial simplification problems on the IBEW exam, you're being tested on your ability to combine like terms—terms that have identical variable parts with the same exponents. To solve this problem, you need to identify and group the like terms in ab−bc+ac−3ab+2bcab - bc + ac - 3ab + 2bc. The like terms are those with the same variable combinations: abab terms, bcbc terms, and acac terms. Group the like terms:
  • abab terms: ab−3ab=−2abab - 3ab = -2ab
  • bcbc terms: −bc+2bc=bc-bc + 2bc = bc
  • acac terms: acac (only one term, so it stays as is)
Combining these gives you −2ab+bc+ac-2ab + bc + ac, which matches answer choice C. Let's examine why the other options are incorrect. Answer A gives −2ab+3bc+ac-2ab + 3bc + ac—this incorrectly adds the bcbc terms as −1+2=3-1 + 2 = 3 instead of 11. Answer B shows −2ab−bc+ac-2ab - bc + ac, which fails to properly combine the bcbc terms, keeping the negative sign from the original −bc-bc term. Answer D presents −3ab+2bc+ac-3ab + 2bc + ac, which leaves the terms uncombined rather than simplifying ab−3abab - 3ab to −2ab-2ab. Remember this key strategy: always identify like terms first, then carefully track positive and negative signs when combining coefficients. Double-check your arithmetic on each group of like terms—sign errors are the most common mistakes in polynomial simplification problems.

Question 9

What is the simplified form of x2−3x+4−(2x2+5x−3)x^2 - 3x + 4 - (2x^2 + 5x - 3)?

  1. 3x2+2x+13x^2 + 2x + 1
  2. −x2+2x+1-x^2 + 2x + 1
  3. −x2−8x+7-x^2 - 8x + 7 (correct answer)
  4. −x2−8x+1-x^2 - 8x + 1
Explanation: This question tests your ability to simplify polynomial expressions by distributing negative signs and combining like terms—a fundamental skill you'll use throughout electrical calculations involving formulas and equations. To solve x2−3x+4−(2x2+5x−3)x^2 - 3x + 4 - (2x^2 + 5x - 3), you must first distribute the negative sign to every term inside the parentheses. The expression becomes: x2−3x+4−2x2−5x+3x^2 - 3x + 4 - 2x^2 - 5x + 3. Now combine like terms by grouping similar powers of x: (x2−2x2)+(−3x−5x)+(4+3)=−x2−8x+7(x^2 - 2x^2) + (-3x - 5x) + (4 + 3) = -x^2 - 8x + 7. Answer A (3x2+2x+13x^2 + 2x + 1) represents the error of adding instead of subtracting the second polynomial entirely. Answer B (−x2+2x+1-x^2 + 2x + 1) shows the correct x2x^2 term but incorrect signs on the other terms—likely from mixing up which terms get the negative sign. Answer D (−x2−8x+1-x^2 - 8x + 1) gets the first two terms right but makes an error in the constant term, probably by subtracting 3 from 4 instead of adding the positive 3 that results from −(−3)-(-3). The key strategy here is to work methodically: first distribute the negative sign completely, then organize terms by their degree before combining. Don't rush—many errors in polynomial arithmetic come from sign mistakes when distributing. Always double-check that you've applied the negative sign to every term in the parentheses, remembering that subtracting a negative gives you a positive.

Question 10

Simplify: 5(a−b)−2(a+b)5(a-b) - 2(a+b)

  1. 3a−3b3a - 3b
  2. 3a+3b3a + 3b
  3. 3a−7b3a - 7b (correct answer)
  4. 7a−3b7a - 3b
Explanation: This question tests your ability to distribute and combine like terms—a fundamental algebraic skill you'll use constantly in electrical calculations involving circuits, power equations, and formulas. To simplify 5(a−b)−2(a+b)5(a-b) - 2(a+b), you need to distribute each coefficient to the terms inside the parentheses, then combine like terms. First, distribute the 5: 5(a−b)=5a−5b5(a-b) = 5a - 5b. Next, distribute the -2 (note the negative sign): −2(a+b)=−2a−2b-2(a+b) = -2a - 2b. Now you have: 5a−5b−2a−2b5a - 5b - 2a - 2b. Combine like terms by grouping the aa terms and bb terms separately: (5a−2a)+(−5b−2b)=3a−7b(5a - 2a) + (-5b - 2b) = 3a - 7b. Looking at the wrong answers: Choice A (3a−3b3a - 3b) correctly finds 3a3a but incorrectly calculates the bb coefficient—you'd get this if you forgot to distribute the negative sign to the second bb term. Choice B (3a+3b3a + 3b) makes the same distribution error with bb but then also changes the overall sign, perhaps from mishandling the subtraction between the two expressions. Choice D (7a−3b7a - 3b) switches the coefficients—you'd get this if you added instead of subtracted the aa terms (5a+2a=7a5a + 2a = 7a) and made sign errors with the bb terms. Remember: when distributing a negative sign or negative coefficient, it affects every term inside the parentheses. Write out each step clearly to avoid sign errors—they're the most common mistake in algebraic manipulation.

Question 11

Combine like terms to simplify: c−8d+4c+8d−2cc - 8d + 4c + 8d - 2c

  1. 3c3c (correct answer)
  2. 3c−16d3c - 16d
  3. 5c5c
  4. 7c+16d7c + 16d
Explanation: When you encounter algebraic expressions with multiple terms, your goal is to combine like terms—terms that have identical variable parts. This is a fundamental skill you'll use constantly in electrical calculations involving resistance, voltage, and current. To simplify c−8d+4c+8d−2cc - 8d + 4c + 8d - 2c, group the like terms together. The cc terms are: cc, +4c+4c, and −2c-2c. The dd terms are: −8d-8d and +8d+8d. For the cc terms: c+4c−2c=1c+4c−2c=3cc + 4c - 2c = 1c + 4c - 2c = 3c For the dd terms: −8d+8d=0-8d + 8d = 0 Since the dd terms cancel out completely, you're left with just 3c3c. Looking at the wrong answers: Answer B (3c−16d3c - 16d) correctly combines the cc terms but incorrectly adds the dd terms instead of recognizing they cancel out. Answer C (5c5c) makes an error in combining the cc terms—likely adding 1+4=51 + 4 = 5 while forgetting to subtract the 2c2c. Answer D (7c+16d7c + 16d) appears to add all coefficients without proper attention to signs, getting 1+4+2=71 + 4 + 2 = 7 for the cc terms and 8+8=168 + 8 = 16 for the dd terms. The correct answer is A (3c3c). Study tip: Always pay careful attention to positive and negative signs when combining like terms. Write out each step to avoid sign errors, and remember that terms with opposite coefficients can cancel completely.

Question 12

Simplify the expression: a−(b−a)−(a−b)a - (b - a) - (a - b)

  1. a−2ba - 2b
  2. aa (correct answer)
  3. 3a3a
  4. a+2ba + 2b
Explanation: When you encounter algebraic expressions with parentheses and subtraction signs, the key is carefully distributing the negative signs and combining like terms systematically. Let's work through a−(b−a)−(a−b)a - (b - a) - (a - b) step by step. First, distribute the negative sign into each set of parentheses. The expression −(b−a)-(b - a) becomes −b+a-b + a, and −(a−b)-(a - b) becomes −a+b-a + b. So our expression transforms to: a+(−b+a)+(−a+b)a + (-b + a) + (-a + b), which simplifies to a−b+a−a+ba - b + a - a + b. Now combine like terms. You have three aa terms: +a+a−a=a+a + a - a = a. You also have two bb terms: −b+b=0-b + b = 0. Therefore, the final answer is simply aa, which is choice B. Let's examine why the other answers are incorrect. Choice A (a−2ba - 2b) results from incorrectly handling the signs when distributing—likely treating both parenthetical expressions as if they were simply subtracted without proper distribution. Choice C (3a3a) comes from adding all the aa terms without recognizing that one has a negative sign. Choice D (a+2ba + 2b) occurs when you flip the signs on the bb terms incorrectly during distribution. The most common error here is mishandling negative signs when distributing. Remember: when you have a negative sign in front of parentheses, it changes the sign of every term inside. Always write out each step clearly and double-check your sign changes to avoid these algebraic pitfalls.

Question 13

What is the simplified form of the expression 9m+5−12m−79m + 5 - 12m - 7?

  1. −3m−2-3m - 2 (correct answer)
  2. 3m+23m + 2
  3. −3m+12-3m + 12
  4. 21m+1221m + 12
Explanation: When you encounter algebraic expressions with multiple terms, your goal is to combine like terms to simplify. This means grouping terms with the same variable together and combining constants separately. Let's work through 9m+5−12m−79m + 5 - 12m - 7 step by step. First, identify and group the like terms: the mm terms are 9m9m and −12m-12m, while the constants are 55 and −7-7. Combining the mm terms: 9m−12m=−3m9m - 12m = -3m Combining the constants: 5−7=−25 - 7 = -2 Therefore, the simplified expression is −3m−2-3m - 2, which is answer choice A. Looking at the incorrect options, choice B (3m+23m + 2) represents two common sign errors: forgetting that 9−12=−39 - 12 = -3 (not positive 3) and miscalculating 5−75 - 7 as positive 2 instead of negative 2. Choice C (−3m+12-3m + 12) correctly handles the variable terms but incorrectly adds the constants as 5+7=125 + 7 = 12 instead of subtracting. Choice D (21m+1221m + 12) shows a fundamental misunderstanding—adding all coefficients together (9+12=219 + 12 = 21) and all constants together (5+7=125 + 7 = 12) while ignoring the negative signs entirely. For IBEW math problems, always pay careful attention to positive and negative signs, especially when subtracting. Write out each step clearly and double-check your sign operations—this prevents the most common algebraic mistakes on electrical trade exams.

Question 14

Combine like terms in the expression: xy+3x−2y+5xy−4xxy + 3x - 2y + 5xy - 4x

  1. 5x2y−x−2y5x^2y - x - 2y
  2. 5xy−7x−2y5xy - 7x - 2y
  3. 6xy+7x−2y6xy + 7x - 2y
  4. 6xy−x−2y6xy - x - 2y (correct answer)
Explanation: When you encounter algebraic expressions with multiple terms, your goal is to combine "like terms" — terms that have identical variable parts. This is a fundamental skill you'll use constantly in electrical calculations involving formulas and equations. To solve this systematically, first identify and group the like terms in xy+3x−2y+5xy−4xxy + 3x - 2y + 5xy - 4x:
  • Terms with xyxy: xy+5xy=6xyxy + 5xy = 6xy
  • Terms with xx: 3x−4x=−x3x - 4x = -x
  • Terms with yy: −2y-2y (stands alone)
Combining these gives you 6xy−x−2y6xy - x - 2y, which matches answer choice D. Let's examine why the other options are incorrect. Choice A (5x2y−x−2y5x^2y - x - 2y) incorrectly shows x2yx^2y instead of xyxy — this suggests confusion about exponents, as xyxy terms don't become x2yx^2y when added. Choice B (5xy−7x−2y5xy - 7x - 2y) correctly identifies the yy term but makes two errors: it gets 5xy5xy instead of 6xy6xy (likely forgetting that xyxy has an implied coefficient of 1), and shows −7x-7x instead of −x-x (possibly adding 3x3x and 4x4x instead of subtracting). Choice C (6xy+7x−2y6xy + 7x - 2y) gets the xyxy term right but shows +7x+7x instead of −x-x, suggesting sign errors when combining 3x−4x3x - 4x. Remember this pattern: always identify like terms first, then combine their coefficients carefully, paying close attention to positive and negative signs. This systematic approach prevents the sign errors that create most wrong answers.

Question 15

Find the simplified form of 3x−2y+z+3y−2x−3z3x - 2y + z + 3y - 2x - 3z.

  1. x−y+2zx - y + 2z
  2. 5x+5y−4z5x + 5y - 4z
  3. x+y−2zx + y - 2z (correct answer)
  4. x+5y−4zx + 5y - 4z
Explanation: When you encounter algebraic expressions with multiple terms, your goal is to combine like terms—terms that have the same variables raised to the same powers. This process, called simplification, is fundamental for solving electrical circuit equations where you'll often work with multiple voltage drops, currents, or resistances. Let's organize the given expression by grouping like terms: 3x−2y+z+3y−2x−3z3x - 2y + z + 3y - 2x - 3z Group the x terms: 3x−2x=1x=x3x - 2x = 1x = x Group the y terms: −2y+3y=1y=y-2y + 3y = 1y = y Group the z terms: z−3z=−2zz - 3z = -2z Combining these results gives us x+y−2zx + y - 2z, which matches answer choice C. Let's examine why the other options are incorrect. Answer A (x−y+2zx - y + 2z) gets the x coefficient right but incorrectly shows −y-y instead of +y+y, and +2z+2z instead of −2z-2z—this suggests errors in combining the y and z terms. Answer B (5x+5y−4z5x + 5y - 4z) appears to add all coefficients rather than properly combining like terms; for instance, treating 3x−2x3x - 2x as 5x5x instead of xx. Answer D (x+5y−4zx + 5y - 4z) correctly finds the x term but makes the same coefficient addition errors for the y and z terms as answer B. Study tip: Always organize your work by grouping like terms first, then carefully track positive and negative signs when combining coefficients. This systematic approach prevents sign errors and ensures you don't miss any terms—skills essential for analyzing electrical circuits with multiple components.

Question 16

Which expression is equivalent to 6<i>x</i>+3<i>y</i>−<i>x</i>−5<i>y</i>6<i>x</i> + 3<i>y</i> - <i>x</i> - 5<i>y</i>?

  1. 5<i>x</i><i>y</i>−25<i>x</i><i>y</i> - 2
  2. 5<i>x</i>+2<i>y</i>5<i>x</i> + 2<i>y</i>
  3. 6<i>x</i>−2<i>y</i>6<i>x</i> - 2<i>y</i>
  4. 5<i>x</i>−2<i>y</i>5<i>x</i> - 2<i>y</i> (correct answer)
Explanation: This question tests the ability to simplify polynomials by combining like terms, a fundamental algebraic skill essential for solving equations. Polynomials consist of terms that can be combined if they share the same variable and exponent, known as like terms. Combining like terms involves summing their coefficients. In this example, the terms 6x and -x are like terms, so their coefficients are added to yield 5x, while 3y and -5y combine to -2y. The correct answer is 5x - 2y because it accurately combines the coefficients of like terms and maintains the original variable and exponent structure. A common distractor might suggest 5x + 2y, which incorrectly adds instead of subtracting coefficients for the y terms, reflecting a misunderstanding of combining like terms. To help students: Emphasize identifying like terms by focusing on variable and exponent matching. Practice with varied examples to reinforce addition of coefficients. Warn against common errors such as unnecessary multiplication or sign changes.

Question 17

Combine like terms in 13<i>x</i>−3<i>y</i>−5<i>x</i>+3<i>y</i>13<i>x</i> - 3<i>y</i> - 5<i>x</i> + 3<i>y</i> to simplify it.

  1. 18<i>x</i>18<i>x</i>
  2. 8<i>x</i>+6<i>y</i>8<i>x</i> + 6<i>y</i>
  3. 8<i>x</i>8<i>x</i> (correct answer)
  4. −8<i>x</i>-8<i>x</i>
Explanation: This question tests the ability to simplify polynomials by combining like terms, a fundamental algebraic skill essential for solving equations. Polynomials consist of terms that can be combined if they share the same variable and exponent, known as like terms. Combining like terms involves summing their coefficients. In this example, the terms 13x and -5x combine to 8x, while -3y and 3y combine to 0y, leaving 8x. The correct answer is 8x because it accurately combines the coefficients of like terms and maintains the original variable and exponent structure. A common distractor might suggest 8x + 6y, which adds non-existent terms, reflecting a misunderstanding of cancellation. To help students: Emphasize identifying like terms by focusing on variable and exponent matching. Practice with varied examples to reinforce addition of coefficients and warn against common errors such as retaining zero terms or sign errors.

Question 18

Combine like terms in 2<i>x</i>+3<i>y</i>+8<i>x</i>−5<i>y</i>2<i>x</i> + 3<i>y</i> + 8<i>x</i> - 5<i>y</i> to simplify it.

  1. 10<i>xy</i>−2<i>y</i>10<i>xy</i> - 2<i>y</i>
  2. 16<i>x</i>−2<i>y</i>16<i>x</i> - 2<i>y</i>
  3. 10<i>x</i>+8<i>y</i>10<i>x</i> + 8<i>y</i>
  4. 10<i>x</i>−2<i>y</i>10<i>x</i> - 2<i>y</i> (correct answer)
Explanation: This question tests the ability to simplify polynomials by combining like terms, a fundamental algebraic skill essential for solving equations. Polynomials consist of terms that can be combined if they share the same variable and exponent, known as like terms. Combining like terms involves summing their coefficients. In this example, the terms 2x and 8x combine to 10x, while 3y and -5y combine to -2y. The correct answer is 10x - 2y because it accurately combines the coefficients of like terms and maintains the original variable and exponent structure. A common distractor might suggest 16x - 2y, which incorrectly adds extra values, reflecting a misunderstanding of coefficient summation. To help students: Emphasize identifying like terms by focusing on variable and exponent matching. Practice with varied examples to reinforce addition of coefficients and warn against common errors such as multiplying terms or changing signs incorrectly.

Question 19

If 6<i>x</i>−4<i>y</i>+5<i>y</i>−9<i>x</i>6<i>x</i> - 4<i>y</i> + 5<i>y</i> - 9<i>x</i> is simplified, what is the coefficient of <i>y</i><i>y</i>?

  1. −9-9
  2. 11 (correct answer)
  3. −1-1
  4. 00
Explanation: This question tests the ability to simplify polynomials by combining like terms, a fundamental algebraic skill essential for solving equations. Polynomials consist of terms that can be combined if they share the same variable and exponent, known as like terms. Combining like terms involves summing their coefficients. In this example, the terms 6x and -9x combine to -3x, while -4y and 5y combine to y, so the coefficient of y is 1. The correct answer is 1 because it accurately identifies the combined coefficient of y after simplifying the expression. A common distractor might suggest -9, which confuses x with y, reflecting a misunderstanding of variable separation. To help students: Emphasize identifying like terms by focusing on variable and exponent matching. Practice with varied examples to reinforce addition of coefficients and warn against common errors such as mixing coefficients or ignoring positives.

Question 20

What is the simplified form of 12<i>x</i>−5<i>x</i>−3<i>y</i>+7<i>y</i>12<i>x</i> - 5<i>x</i> - 3<i>y</i> + 7<i>y</i>?

  1. 7<i>x</i>−10<i>y</i>7<i>x</i> - 10<i>y</i>
  2. 17<i>x</i>+4<i>y</i>17<i>x</i> + 4<i>y</i>
  3. 7<i>x</i>+4<i>y</i>7<i>x</i> + 4<i>y</i> (correct answer)
  4. 60<i>x</i>+4<i>y</i>60<i>x</i> + 4<i>y</i>
Explanation: This question tests the ability to simplify polynomials by combining like terms, a fundamental algebraic skill essential for solving equations. Polynomials consist of terms that can be combined if they share the same variable and exponent, known as like terms. Combining like terms involves summing their coefficients. In this example, the terms 12x and -5x combine to 7x, while -3y and 7y combine to 4y. The correct answer is 7x + 4y because it accurately combines the coefficients of like terms and maintains the original variable and exponent structure. A common distractor might suggest 17x + 4y, which incorrectly subtracts in reverse, reflecting a misunderstanding of negative coefficients. To help students: Emphasize identifying like terms by focusing on variable and exponent matching. Practice with varied examples to reinforce addition of coefficients and warn against common errors such as sign mishandling or unnecessary multiplication.