Home

Tutoring

Subjects

Live Classes

Study Coach

Essay Review

On-Demand Courses

Colleges

Games

Sign up

Log in

Opening subject page...

Loading your content

Practice

  • All Subjects
  • Algebra Flashcards
  • SAT Math Practice Tests
  • Math Question of the Day
  • Live Classes
  • On-Demand Courses

Varsity Tutors

  • Find a Tutor
  • Test Prep
  • Online Classes
  • K-12 Learning
  • College Search
  • VarsityTutors.com

© 2026 Varsity Tutors. All rights reserved.

← Back to quizzes

College Algebra Quiz

College Algebra Quiz: Simplifying Algebraic Expressions

Practice Simplifying Algebraic Expressions in College Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

Question 1 / 20

0 of 20 answered

Using the distributive property and combining like terms, which expression is equivalent to 5(x−2)−3(x+4)5(x-2)-3(x+4)5(x−2)−3(x+4)?

Select an answer to continue

What this quiz covers

This quiz focuses on Simplifying Algebraic Expressions, giving you a quick way to practice the rules, question types, and explanations that matter most for College Algebra.

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 the distributive property and combining like terms, which expression is equivalent to 5(x−2)−3(x+4)5(x-2)-3(x+4)5(x−2)−3(x+4)?

  1. 2x−222x-222x−22 (correct answer)
  2. 2x+22x+22x+2
  3. 8x−228x-228x−22
  4. 2x−22x-22x−2

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 2

Simplify the expression using exponent rules: (2x2)(3x4)(2x^2)(3x^4)(2x2)(3x4).

  1. 6x66x^66x6 (correct answer)
  2. 5x85x^85x8
  3. 6x86x^86x8
  4. 6x26x^26x2

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 3

Simplify the complex fraction: 2356\dfrac{\tfrac{2}{3}}{\tfrac{5}{6}}65​32​​ using reciprocal multiplication.

  1. 45\dfrac{4}{5}54​ (correct answer)
  2. 54\dfrac{5}{4}45​
  3. 1215\dfrac{12}{15}1512​
  4. 1018\dfrac{10}{18}1810​

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 4

Simplify the radical expression using product properties: 18x2\sqrt{18x^2}18x2​ for x≥0x\ge 0x≥0.

  1. 3x23x\sqrt{2}3x2​ (correct answer)
  2. 9x29x\sqrt{2}9x2​
  3. 32x23\sqrt{2x^2}32x2​
  4. 18x2\sqrt{18}x^218​x2

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 5

Factor the trinomial using special products: x2+10x+25x^2+10x+25x2+10x+25.

  1. (x+5)2(x+5)^2(x+5)2 (correct answer)
  2. (x−5)2(x-5)^2(x−5)2
  3. (x+25)(x+1)(x+25)(x+1)(x+25)(x+1)
  4. (x+5)(x−5)(x+5)(x-5)(x+5)(x−5)

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 6

Simplify the expression using distribution and like terms: −2(3x−4)+x-2(3x-4)+x−2(3x−4)+x.

  1. −5x+8-5x+8−5x+8 (correct answer)
  2. −7x−8-7x-8−7x−8
  3. −5x−8-5x-8−5x−8
  4. −7x+8-7x+8−7x+8

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 7

Factor using the difference of squares pattern: x2−16x^2-16x2−16.

  1. (x−4)(x+4)(x-4)(x+4)(x−4)(x+4) (correct answer)
  2. (x−8)(x+2)(x-8)(x+2)(x−8)(x+2)
  3. (x−4)2(x-4)^2(x−4)2
  4. (x+4)2(x+4)^2(x+4)2

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 8

Apply exponent rules for real numbers to simplify: x3⋅x5x^3\cdot x^5x3⋅x5.

  1. x15x^{15}x15
  2. x8x^8x8 (correct answer)
  3. x2x^2x2
  4. 2x82x^82x8

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 9

Simplify the radical expression using real-number properties: 50\sqrt{50}50​.

  1. 525\sqrt{2}52​ (correct answer)
  2. 25225\sqrt{2}252​
  3. 25\sqrt{25}25​
  4. 10510\sqrt{5}105​

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 10

Which expression is equivalent to 2(3x+1)−4(x−2)2(3x+1)-4( x-2)2(3x+1)−4(x−2) after simplifying?

  1. 2x+102x+102x+10 (correct answer)
  2. 2x−62x-62x−6
  3. 10x+210x+210x+2
  4. 2x+22x+22x+2

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 11

Use order of operations to simplify: 4+3(22)−54+3(2^2)-54+3(22)−5.

  1. 111111 (correct answer)
  2. 151515
  3. 777
  4. 202020

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 12

Rationalize the denominator using a conjugate: 53\dfrac{5}{\sqrt{3}}3​5​.

  1. 533\dfrac{5\sqrt{3}}{3}353​​ (correct answer)
  2. 533\dfrac{5}{3\sqrt{3}}33​5​
  3. 35\dfrac{\sqrt{3}}{5}53​​
  4. 153\dfrac{15}{\sqrt{3}}3​15​

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 13

Simplify using the distributive property and additive inverses: 7−(3x−5)+2x7-(3x-5)+2x7−(3x−5)+2x.

  1. 5x+125x+125x+12
  2. −x+12-x+12−x+12 (correct answer)
  3. −x−12-x-12−x−12
  4. 5x−125x-125x−12

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 14

Given that a=2xa = 2^xa=2x and b=3xb = 3^xb=3x, express 6x+6x+16^x + 6^{x+1}6x+6x+1 in terms of aaa and bbb.

  1. ab+6abab + 6abab+6ab
  2. 7ab7ab7ab (correct answer)
  3. ab+ab2ab + ab^2ab+ab2
  4. a+b+6aba + b + 6aba+b+6ab

Explanation: First, note that 6x=(2⋅3)x=2x⋅3x=ab6^x = (2 \cdot 3)^x = 2^x \cdot 3^x = ab6x=(2⋅3)x=2x⋅3x=ab. Also, 6x+1=6x⋅61=6⋅6x=6ab6^{x+1} = 6^x \cdot 6^1 = 6 \cdot 6^x = 6ab6x+1=6x⋅61=6⋅6x=6ab. Therefore: 6x+6x+1=ab+6ab=7ab6^x + 6^{x+1} = ab + 6ab = 7ab6x+6x+1=ab+6ab=7ab. Choice A shows the intermediate step but doesn't combine like terms. Choice C incorrectly treats the exponent x+1x+1x+1 as affecting only the base 3. Choice D incorrectly adds separate aaa and bbb terms that don't correspond to the original expression.

Question 15

Factor the trinomial using integer factoring: x2−5x+6x^2-5x+6x2−5x+6.

  1. (x−2)(x−3)(x-2)(x-3)(x−2)(x−3) (correct answer)
  2. (x+2)(x+3)(x+2)(x+3)(x+2)(x+3)
  3. (x−1)(x−6)(x-1)(x-6)(x−1)(x−6)
  4. (x−2)2(x-2)^2(x−2)2

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 16

Simplify by combining like terms: 34x+12x\dfrac{3}{4}x+\dfrac{1}{2}x43​x+21​x.

  1. 54x\dfrac{5}{4}x45​x (correct answer)
  2. 46x\dfrac{4}{6}x64​x
  3. 38x\dfrac{3}{8}x83​x
  4. 24x\dfrac{2}{4}x42​x

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 17

Rationalize the denominator by multiplying by the conjugate: 23−5\dfrac{2}{3-\sqrt{5}}3−5​2​.

  1. 3+52\dfrac{3+\sqrt{5}}{2}23+5​​ (correct answer)
  2. 3−52\dfrac{3-\sqrt{5}}{2}23−5​​
  3. 3+54\dfrac{3+\sqrt{5}}{4}43+5​​
  4. 6+254\dfrac{6+2\sqrt{5}}{4}46+25​​

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 18

Simplify the polynomial by factoring a greatest common factor: 6x2−9x6x^2-9x6x2−9x.

  1. 3x(2x−3)3x(2x-3)3x(2x−3) (correct answer)
  2. 6x(x−3)6x( x-3)6x(x−3)
  3. 3(2x−3)3(2x-3)3(2x−3)
  4. x(6x−9x)x(6x-9x)x(6x−9x)

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 19

Using rational exponents and exponent rules, simplify (x12)4\left(x^{\tfrac{1}{2}}\right)^4(x21​)4 for x≥0x\ge 0x≥0.

  1. x2x^2x2 (correct answer)
  2. x18x^{\tfrac{1}{8}}x81​
  3. x32x^{\tfrac{3}{2}}x23​
  4. 4x124x^{\tfrac{1}{2}}4x21​

Explanation: This question tests college-level algebra skills in simplifying algebraic expressions. Simplifying involves using properties of real numbers and order of operations to reduce expressions to their simplest form. For example, combining like terms and factoring are essential steps. The correct answer demonstrates accurate simplification by applying these principles, such as correctly distributing and combining terms. A common mistake is incorrectly applying the order of operations, leading to erroneous results. Teach students to carefully follow order of operations and check their work by substituting values to verify equivalence. Encourage practice with varied expressions to strengthen understanding.

Question 20

Factor completely: 6x4−54x26x^4 - 54x^26x4−54x2

  1. 6x2(x2−9)6x^2(x^2 - 9)6x2(x2−9)
  2. 6x2(x−3)(x+3)6x^2(x - 3)(x + 3)6x2(x−3)(x+3) (correct answer)
  3. 6x2(x−3)26x^2(x - 3)^26x2(x−3)2
  4. 6(x2−3)(x2+3)6(x^2 - 3)(x^2 + 3)6(x2−3)(x2+3)

Explanation: First factor out the GCF: 6x4−54x2=6x2(x2−9)6x^4 - 54x^2 = 6x^2(x^2 - 9)6x4−54x2=6x2(x2−9). Then recognize that x2−9x^2 - 9x2−9 is a difference of squares: x2−9=(x−3)(x+3)x^2 - 9 = (x-3)(x+3)x2−9=(x−3)(x+3). Therefore, the complete factorization is 6x2(x−3)(x+3)6x^2(x-3)(x+3)6x2(x−3)(x+3). Choice A stops at partial factoring. Choice C incorrectly factors x2−9x^2-9x2−9 as (x−3)2(x-3)^2(x−3)2. Choice D factors out 6 instead of 6x26x^26x2 and uses an incorrect difference of squares pattern.