IBEW: Electrical Training Alliance Aptitude Test Quiz: Multiply Factored Expressions
20 questions · exam conditions
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Multiply Factored ExpressionsQuestion 1 of 20

Using distribution, expand (x+3)(x+5)(x + 3)(x + 5) to a polynomial.

x3+8x+15x^3 + 8x + 15
x2+15x+8x^2 + 15x + 8
x2+8xx^2 + 8x
x2+8x+15x^2 + 8x + 15
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IBEW: Electrical Training Alliance Aptitude Test Quiz

IBEW: Electrical Training Alliance Aptitude Test Quiz: Multiply Factored Expressions

Practice Multiply Factored Expressions 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 Multiply Factored Expressions, 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

Using distribution, expand (x+3)(x+5)(x + 3)(x + 5) to a polynomial.

  1. x3+8x+15x^3 + 8x + 15
  2. x2+15x+8x^2 + 15x + 8
  3. x2+8xx^2 + 8x
  4. x2+8x+15x^2 + 8x + 15 (correct answer)
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (x + 3)(x + 5), each term in the first binomial is multiplied by each term in the second, resulting in x^2 + 5x + 3x + 15. The correct answer is 'x^2 + 8x + 15' because combining the like terms 5x and 3x gives 8x. A common error is failing to multiply each term correctly, leading to incorrect answers such as 'x^2 + 3x + 5'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 2

Using distribution, expand (9x+2)(x+1)(9x + 2)(x + 1) correctly.

  1. 9x2+2x+19x^2 + 2x + 1
  2. 9x2+9x+29x^2 + 9x + 2
  3. 9x2+11x+19x^2 + 11x + 1
  4. 9x2+11x+29x^2 + 11x + 2 (correct answer)
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (9x + 2)(x + 1), each term in the first binomial is multiplied by each term in the second, resulting in 9x^2 + 9x + 2x + 2. The correct answer is '9x^2 + 11x + 2' because combining the like terms 9x and 2x gives 11x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '9x^2 + 9x + 2'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 3

Expand (2x+1)(2x+5)(2x + 1)(2x + 5) and combine like terms.

  1. 4x2+12x+64x^2 + 12x + 6
  2. 4x2+10x+54x^2 + 10x + 5
  3. 4x2+12x+54x^2 + 12x + 5 (correct answer)
  4. 4x2+54x^2 + 5
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (2x + 1)(2x + 5), each term in the first binomial is multiplied by each term in the second, resulting in 4x^2 + 10x + 2x + 5. The correct answer is '4x^2 + 12x + 5' because combining the like terms 10x and 2x gives 12x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '4x^2 + 10x + 5'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 4

In analyzing a circuit, an expression (I+3)(2I−1)(I + 3)(2I - 1) arises. What is this expression when expanded?

  1. 3I+23I + 2
  2. 2I2−5I−32I^2 - 5I - 3
  3. 2I2+7I−32I^2 + 7I - 3
  4. 2I2+5I−32I^2 + 5I - 3 (correct answer)
Explanation: When you encounter algebraic expressions in electrical circuit analysis, you'll often need to expand products of binomials. This tests your ability to apply the distributive property systematically. To expand (I+3)(2I−1)(I + 3)(2I - 1), you multiply each term in the first binomial by each term in the second binomial. Using the FOIL method: First terms: I×2I=2I2I \times 2I = 2I^2. Outer terms: I×(−1)=−II \times (-1) = -I. Inner terms: 3×2I=6I3 \times 2I = 6I. Last terms: 3×(−1)=−33 \times (-1) = -3. Combining these gives: 2I2−I+6I−3=2I2+5I−32I^2 - I + 6I - 3 = 2I^2 + 5I - 3. Answer choice A (3I+23I + 2) completely ignores the quadratic nature of multiplying two linear expressions and appears to result from incorrectly adding coefficients rather than multiplying terms. Answer choice B (2I2−5I−32I^2 - 5I - 3) gets the quadratic and constant terms correct but has the wrong sign on the linear term—this suggests combining −I+6I-I + 6I as −5I-5I instead of +5I+5I. Answer choice C (2I2+7I−32I^2 + 7I - 3) correctly identifies the quadratic and constant terms but miscalculates the middle term, possibly by adding 1+6=71 + 6 = 7 instead of properly handling −1+6=5-1 + 6 = 5. The key strategy is to be methodical with FOIL and carefully track positive and negative signs when combining like terms. Double-check your arithmetic on the middle term, as sign errors there are the most common mistake in binomial multiplication.

Question 5

Find the expanded result of (7x+3)(x+2)(7x + 3)(x + 2).

  1. 7x2+17x+57x^2 + 17x + 5
  2. 7x2+14x+67x^2 + 14x + 6
  3. 7x2+17x+67x^2 + 17x + 6 (correct answer)
  4. 7x2+67x^2 + 6
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (7x + 3)(x + 2), each term in the first binomial is multiplied by each term in the second, resulting in 7x^2 + 14x + 3x + 6. The correct answer is '7x^2 + 17x + 6' because combining the like terms 14x and 3x gives 17x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '7x^2 + 14x + 6'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 6

Simplify (8x+1)(x+3)(8x + 1)(x + 3) by multiplying terms.

  1. 8x3+25x+38x^3 + 25x + 3
  2. 8x2+24x+38x^2 + 24x + 3
  3. 8x2+25x+48x^2 + 25x + 4
  4. 8x2+25x+38x^2 + 25x + 3 (correct answer)
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (8x + 1)(x + 3), each term in the first binomial is multiplied by each term in the second, resulting in 8x^2 + 24x + x + 3. The correct answer is '8x^2 + 25x + 3' because combining the like terms 24x and x gives 25x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '8x^2 + 24x + 3'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 7

Expand (2x+3)(4x+1)(2x + 3)(4x + 1) and simplify completely.

  1. 8x2+14x+48x^2 + 14x + 4
  2. 8x2+12x+38x^2 + 12x + 3
  3. 8x2+14x+38x^2 + 14x + 3 (correct answer)
  4. 8x3+14x+38x^3 + 14x + 3
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (2x + 3)(4x + 1), each term in the first binomial is multiplied by each term in the second, resulting in 8x^2 + 2x + 12x + 3. The correct answer is '8x^2 + 14x + 3' because combining the like terms 2x and 12x gives 14x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '8x^2 + 12x + 3'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 8

The original dimensions of a rectangular junction box are (L)(L) by (W)(W). If the length is increased by 4 units and the width is increased by 2 units, which expression represents the new area?

  1. LW+8LW + 8
  2. L+W+6L + W + 6
  3. LW+6LW + 6
  4. LW+2L+4W+8LW + 2L + 4W + 8 (correct answer)
Explanation: When you encounter area problems involving dimensional changes, you need to apply the distributive property systematically to account for how both dimensions affect the total area. The original area is L×W=LWL \times W = LW. After increasing the length by 4 units and width by 2 units, the new dimensions become (L+4)(L + 4) and (W+2)(W + 2). To find the new area, you multiply these expressions: (L+4)(W+2)=L(W+2)+4(W+2)=LW+2L+4W+8(L + 4)(W + 2) = L(W + 2) + 4(W + 2) = LW + 2L + 4W + 8 This expansion shows the new area consists of four parts: the original area (LWLW), plus the additional area from extending the length (2L2L), plus the additional area from extending the width (4W4W), plus the corner rectangle created by both extensions (88). Choice A (LW+8LW + 8) incorrectly assumes only the corner area is added, ignoring the rectangular strips along the extended sides. Choice B (L+W+6L + W + 6) confuses area with perimeter calculations and represents a linear measurement rather than area. Choice C (LW+6LW + 6) adds the dimension increases directly to the original area, which doesn't account for how area scales with both dimensions. The correct answer is D: LW+2L+4W+8LW + 2L + 4W + 8. Study tip: For area expansion problems, always use FOIL or the distributive property to multiply the new dimensions completely. Don't try to shortcut by just adding the increases to the original area—you'll miss the interaction terms that represent the extended rectangular regions.

Question 9

Multiply (6x+2)(x+5)(6x + 2)(x + 5) and write the expanded form.

  1. 6x2+30x+106x^2 + 30x + 10
  2. 6x2+12x+106x^2 + 12x + 10
  3. 6x2+32x+106x^2 + 32x + 10 (correct answer)
  4. 6x2+32x6x^2 + 32x
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (6x + 2)(x + 5), each term in the first binomial is multiplied by each term in the second, resulting in 6x^2 + 30x + 2x + 10. The correct answer is '6x^2 + 32x + 10' because combining the like terms 30x and 2x gives 32x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '6x^2 + 30x + 10'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 10

Expand (2x+9)(x+4)(2x + 9)(x + 4) and combine like terms.

  1. 2x2+17x+132x^2 + 17x + 13
  2. 2x2+8x+362x^2 + 8x + 36
  3. 2x2+17x+362x^2 + 17x + 36 (correct answer)
  4. 2x2+362x^2 + 36
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (2x + 9)(x + 4), each term in the first binomial is multiplied by each term in the second, resulting in 2x^2 + 8x + 9x + 36. The correct answer is '2x^2 + 17x + 36' because combining the like terms 8x and 9x gives 17x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '2x^2 + 8x + 36'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 11

Multiply (x+8)(x+1)(x + 8)(x + 1) and simplify the result.

  1. x2+8x^2 + 8
  2. x2+8x+1x^2 + 8x + 1
  3. x2+9xx^2 + 9x
  4. x2+9x+8x^2 + 9x + 8 (correct answer)
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (x + 8)(x + 1), each term in the first binomial is multiplied by each term in the second, resulting in x^2 + x + 8x + 8. The correct answer is 'x^2 + 9x + 8' because combining the like terms x and 8x gives 9x. A common error is failing to multiply each term correctly, leading to incorrect answers such as 'x^2 + 8x + 1'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 12

Simplify the expression −2(n−3)(n−4)-2(n - 3)(n - 4).

  1. n2−7n+12n^2 - 7n + 12
  2. −2n2−14n−24-2n^2 - 14n - 24
  3. −2n2+14n−24-2n^2 + 14n - 24 (correct answer)
  4. −2n2+7n+12-2n^2 + 7n + 12
Explanation: When you encounter expressions with multiple factors like this, you need to systematically expand using the distributive property. Start by multiplying the two binomials, then distribute the coefficient. First, expand (n−3)(n−4)(n - 3)(n - 4) using FOIL:
  • First terms: n⋅n=n2n \cdot n = n^2
  • Outer terms: n⋅(−4)=−4nn \cdot (-4) = -4n
  • Inner terms: (−3)⋅n=−3n(-3) \cdot n = -3n
  • Last terms: (−3)⋅(−4)=12(-3) \cdot (-4) = 12
This gives you n2−4n−3n+12=n2−7n+12n^2 - 4n - 3n + 12 = n^2 - 7n + 12. Now distribute the −2-2: −2(n2−7n+12)=−2n2+14n−24-2(n^2 - 7n + 12) = -2n^2 + 14n - 24, which is answer C. Let's examine why the other options are wrong. Answer A (n2−7n+12n^2 - 7n + 12) is just the expanded binomial product without applying the −2-2 coefficient. Answer B (−2n2−14n−24-2n^2 - 14n - 24) makes a sign error when distributing the −2-2 to the middle term—it should be +14n+14n, not −14n-14n. Answer D (−2n2+7n+12-2n^2 + 7n + 12) fails to distribute the −2-2 to all terms correctly, keeping the middle and last terms as if the coefficient were −1-1 instead of −2-2. The key strategy here is to work step-by-step and track your signs carefully. Expand the binomials first, combine like terms, then distribute any outside coefficients. Sign errors are the most common mistake in these problems, so double-check each step.

Question 13

Expand the expression (4x+y)(2x−3y)(4x + y)(2x - 3y).

  1. 8x2−10xy−3y28x^2 - 10xy - 3y^2 (correct answer)
  2. 8x2−14xy−3y28x^2 - 14xy - 3y^2
  3. 8x2+10xy−3y28x^2 + 10xy - 3y^2
  4. 8x2−3y28x^2 - 3y^2
Explanation: When you encounter polynomial multiplication like this, you're using the distributive property (also called FOIL for binomials). You need to multiply each term in the first expression by each term in the second expression. Let's expand (4x+y)(2x−3y)(4x + y)(2x - 3y) systematically: First, multiply 4x4x by each term in the second parentheses:
  • 4x⋅2x=8x24x \cdot 2x = 8x^2
  • 4x⋅(−3y)=−12xy4x \cdot (-3y) = -12xy
Next, multiply yy by each term in the second parentheses:
  • y⋅2x=2xyy \cdot 2x = 2xy
  • y⋅(−3y)=−3y2y \cdot (-3y) = -3y^2
Now combine all terms: 8x2−12xy+2xy−3y28x^2 - 12xy + 2xy - 3y^2 Combine like terms: 8x2+(−12xy+2xy)−3y2=8x2−10xy−3y28x^2 + (-12xy + 2xy) - 3y^2 = 8x^2 - 10xy - 3y^2 Looking at the wrong answers: Answer B gives −14xy-14xy instead of −10xy-10xy, which happens if you incorrectly combine the middle terms as −12xy−2xy-12xy - 2xy instead of −12xy+2xy-12xy + 2xy. Answer C shows +10xy+10xy, which occurs if you miss the negative sign when multiplying 4x⋅(−3y)4x \cdot (-3y). Answer D completely omits the middle term, suggesting someone tried to use the difference of squares formula incorrectly—that only works for expressions like (a+b)(a−b)(a+b)(a-b), not (4x+y)(2x−3y)(4x+y)(2x-3y). The correct answer is A: 8x2−10xy−3y28x^2 - 10xy - 3y^2. Study tip: Always write out every multiplication step when expanding polynomials. The most common errors happen when combining like terms or handling negative signs, so double-check your arithmetic on the middle terms.

Question 14

Find the product of (2x+13)(x−12)(2x + \frac{1}{3})(x - \frac{1}{2}).

  1. 2x2+23x−162x^2 + \frac{2}{3}x - \frac{1}{6}
  2. 2x2−23x−162x^2 - \frac{2}{3}x - \frac{1}{6} (correct answer)
  3. 2x2−x−162x^2 - x - \frac{1}{6}
  4. 2x2−162x^2 - \frac{1}{6}
Explanation: When you encounter polynomial multiplication problems like this one, you're applying the distributive property (also called FOIL for binomials). This means multiplying each term in the first expression by each term in the second expression. To find (2x+13)(x−12)(2x + \frac{1}{3})(x - \frac{1}{2}), you need to multiply systematically: First terms: 2x⋅x=2x22x \cdot x = 2x^2 Outer terms: 2x⋅(−12)=−x2x \cdot (-\frac{1}{2}) = -x Inner terms: 13⋅x=13x\frac{1}{3} \cdot x = \frac{1}{3}x Last terms: 13⋅(−12)=−16\frac{1}{3} \cdot (-\frac{1}{2}) = -\frac{1}{6} Combining these: 2x2−x+13x−162x^2 - x + \frac{1}{3}x - \frac{1}{6} The middle terms combine: −x+13x=−33x+13x=−23x-x + \frac{1}{3}x = -\frac{3}{3}x + \frac{1}{3}x = -\frac{2}{3}x Final result: 2x2−23x−162x^2 - \frac{2}{3}x - \frac{1}{6}, which is answer B. Looking at the wrong answers: Answer A has +23x+\frac{2}{3}x instead of −23x-\frac{2}{3}x, which happens when you incorrectly handle the negative signs during multiplication. Answer C shows −x-x instead of −23x-\frac{2}{3}x, indicating the middle terms weren't properly combined. Answer D is missing the middle term entirely, suggesting only the first and last terms were multiplied. Study tip: When multiplying binomials with fractions, work slowly through each step and pay special attention to signs. Convert whole number coefficients to fractions with common denominators when combining like terms—this prevents arithmetic errors that are common on electrical worker exams.

Question 15

Find the expanded form of (3x+2)(x+7)(3x + 2)(x + 7).

  1. 3x2+21x+143x^2 + 21x + 14
  2. 3x2+9x+143x^2 + 9x + 14
  3. 3x2+23x+143x^2 + 23x + 14 (correct answer)
  4. 3x3+23x+143x^3 + 23x + 14
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (3x + 2)(x + 7), each term in the first binomial is multiplied by each term in the second, resulting in 3x^2 + 21x + 2x + 14. The correct answer is '3x^2 + 23x + 14' because combining the like terms 21x and 2x gives 23x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '3x^2 + 21x + 14'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 16

Multiply (x+4)(x+7)(x + 4)(x + 7) to get the simplified polynomial.

  1. x3+11x+28x^3 + 11x + 28
  2. x2+28x+11x^2 + 28x + 11
  3. x2+11x+7x^2 + 11x + 7
  4. x2+11x+28x^2 + 11x + 28 (correct answer)
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (x + 4)(x + 7), each term in the first binomial is multiplied by each term in the second, resulting in x^2 + 7x + 4x + 28. The correct answer is 'x^2 + 11x + 28' because combining the like terms 7x and 4x gives 11x. A common error is failing to multiply each term correctly, leading to incorrect answers such as 'x^2 + 28x + 11'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 17

Compute the expanded polynomial for (5x+1)(x+4)(5x + 1)(x + 4).

  1. 5x2+5x+45x^2 + 5x + 4
  2. 5x2+20x+45x^2 + 20x + 4
  3. 5x2+21x+45x^2 + 21x + 4 (correct answer)
  4. 5x2+21x5x^2 + 21x
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (5x + 1)(x + 4), each term in the first binomial is multiplied by each term in the second, resulting in 5x^2 + 20x + x + 4. The correct answer is '5x^2 + 21x + 4' because combining the like terms 20x and x gives 21x. A common error is failing to multiply each term correctly, leading to incorrect answers such as '5x^2 + 20x + 4'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.

Question 18

Which of the following products equals x2−2x−15x^2 - 2x - 15?

  1. (x+5)(x−3)(x + 5)(x - 3)
  2. (x−5)(x+3)(x - 5)(x + 3) (correct answer)
  3. (x+5)(x+3)(x + 5)(x + 3)
  4. (x−5)(x−3)(x - 5)(x - 3)
Explanation: This question tests your ability to factor quadratic expressions, a fundamental algebra skill you'll use regularly in electrical calculations involving power, resistance, and circuit analysis. To solve this, you need to find which factored form expands back to x2−2x−15x^2 - 2x - 15. Use the FOIL method (First, Outer, Inner, Last) to check each option. Let's verify the correct answer by expanding option B: (x−5)(x+3)(x - 5)(x + 3). Using FOIL: First terms give x⋅x=x2x \cdot x = x^2. Outer terms give x⋅3=3xx \cdot 3 = 3x. Inner terms give −5⋅x=−5x-5 \cdot x = -5x. Last terms give −5⋅3=−15-5 \cdot 3 = -15. Combining: x2+3x−5x−15=x2−2x−15x^2 + 3x - 5x - 15 = x^2 - 2x - 15. This matches perfectly. Now let's see why the others fail. Option A: (x+5)(x−3)(x + 5)(x - 3) expands to x2−3x+5x−15=x2+2x−15x^2 - 3x + 5x - 15 = x^2 + 2x - 15. The middle term is positive 2x, not negative 2x. Option C: (x+5)(x+3)(x + 5)(x + 3) gives x2+3x+5x+15=x2+8x+15x^2 + 3x + 5x + 15 = x^2 + 8x + 15. Both the middle term and constant are wrong. Option D: (x−5)(x−3)(x - 5)(x - 3) produces x2−3x−5x+15=x2−8x+15x^2 - 3x - 5x + 15 = x^2 - 8x + 15, which has the wrong middle term and constant. Study tip: When factoring quadratics of the form x2+bx+cx^2 + bx + c, look for two numbers that multiply to give c and add to give b. Here, you needed numbers multiplying to -15 and adding to -2: that's -5 and +3.

Question 19

Expand and simplify (5a−2)(3a−4)(5a - 2)(3a - 4).

  1. 15a2+26a+815a^2 + 26a + 8
  2. 15a2−14a+815a^2 - 14a + 8
  3. 15a2+815a^2 + 8
  4. 15a2−26a+815a^2 - 26a + 8 (correct answer)
Explanation: When you encounter binomial multiplication problems like this, you're applying the distributive property (also called FOIL) to expand two expressions in parentheses. To expand (5a−2)(3a−4)(5a - 2)(3a - 4), multiply each term in the first binomial by each term in the second binomial: First terms: (5a)(3a)=15a2(5a)(3a) = 15a^2 Outer terms: (5a)(−4)=−20a(5a)(-4) = -20a Inner terms: (−2)(3a)=−6a(-2)(3a) = -6a Last terms: (−2)(−4)=+8(-2)(-4) = +8 Combining these: 15a2−20a−6a+8=15a2−26a+815a^2 - 20a - 6a + 8 = 15a^2 - 26a + 8 This matches answer choice D. Let's examine why the other options are incorrect: Answer A gives 15a2+26a+815a^2 + 26a + 8. This results from incorrectly making the middle term positive instead of negative, likely from sign errors when multiplying negative terms. Answer B shows 15a2−14a+815a^2 - 14a + 8. Here, the middle term coefficient is wrong. You'd get -14a if you incorrectly calculated the outer and inner terms as −20a+6a-20a + 6a instead of −20a−6a-20a - 6a. Answer C gives 15a2+815a^2 + 8, completely missing the middle term. This suggests forgetting to multiply the outer and inner terms entirely. Remember this key strategy: When expanding binomials, be extra careful with negative signs and always double-check that you've multiplied all four term combinations. The most common errors on these problems involve sign mistakes or forgetting terms, so work systematically through each multiplication step.

Question 20

Simplify the product (x+9)(x+2)(x + 9)(x + 2) by expansion.

  1. x2+11xx^2 + 11x
  2. x2+18x+11x^2 + 18x + 11
  3. x2+11x+18x^2 + 11x + 18 (correct answer)
  4. x2+18x^2 + 18
Explanation: This question tests the ability to identify and expand products from factored algebraic expressions, a key skill in algebra and functions. The process involves applying the distributive property, multiplying each term in the first polynomial by each term in the second, then combining like terms. For example, in the expression (x + 9)(x + 2), each term in the first binomial is multiplied by each term in the second, resulting in x^2 + 2x + 9x + 18. The correct answer is 'x^2 + 11x + 18' because combining the like terms 2x and 9x gives 11x. A common error is failing to multiply each term correctly, leading to incorrect answers such as 'x^2 + 18x + 11'. Teaching strategies include practicing the distributive property with various expressions, using visual aids like area models to illustrate multiplication, and reinforcing the combination of like terms.