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Quizzes > High School Quizzes > Mathematics

Combining Like Terms Practice Quiz

Master algebra simplification with engaging practice problems

Editorial: Review CompletedCreated By: Kristaps LininsUpdated Aug 23, 2025
Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a challenging high school math trivia quiz.

Use this combining like terms quiz to practice simplifying expressions and check your skills. You'll work through 20 high school questions with like terms, negatives, and parentheses, then see your score so you can spot gaps before the exam or homework. Take it to warm up, build speed, and make each algebra step feel easier.

Simplify: 3x + 2x
x
5
5x
6x
Combining the like terms 3x and 2x gives 5x because you add the coefficients. The variable remains unchanged.
Simplify: 7y - 4y
11y
7y
4y
3y
Subtracting the coefficients of like terms, 7y minus 4y equals 3y. The variable y stays the same during the process.
Simplify: 5a + 3b - 2a
5a - 3b
7a + 3b
3a
3a + 3b
Subtract the like terms 5a and -2a to obtain 3a while the term 3b remains separate. This yields the expression 3a + 3b.
Simplify: x + 2 + 3x
2x + 2
4x
3x + 2
4x + 2
Combine the like terms x and 3x to get 4x, while the constant 2 remains unchanged. The simplified expression is 4x + 2.
Simplify: 10 - 3 + 2y - 5y
7y - 3
7 - 3y
10 - 3y
7 + 3y
First, combine the constants: 10 minus 3 equals 7. Then, combine the y terms: 2y minus 5y equals -3y, resulting in 7 - 3y.
Simplify: 4x + 3 - 2x + 7
6x + 10
2x + 10
2x + 7
4x + 7
Combine the x terms by subtracting 2x from 4x to get 2x, and add the constants 3 and 7 to get 10. This gives the simplified expression 2x + 10.
Combine like terms: 8a + 2b - 3a + 4c - 2b
5a - 4c
5a + 4c
5a + 2b + 4c
11a + 4c
Subtract 3a from 8a to get 5a, and notice that 2b and -2b cancel each other out. The term 4c remains without any like terms, so the answer is 5a + 4c.
Simplify: 2(3x + 4) + 5x
8x + 11
10x + 8
11x + 8
11x + 4
Distribute the 2 over (3x + 4) to obtain 6x + 8, then add the like term 5x. The final simplified form is 11x + 8.
Simplify: 3(2y - 5) - 4(y - 1)
6y - 11
2y - 15
2y + 11
2y - 11
First, distribute to get 6y - 15 from the first term and -4y + 4 from the second term. Then, combine the like terms to obtain 2y - 11.
Combine like terms in: 5x - 2x + 3y + 7 - y - 1
3x + 3y + 6
7x + 6
3x + 2y + 6
3x + 2y + 8
Subtract the x terms (5x - 2x) to get 3x and the y terms (3y - y) to get 2y; add the constants 7 and -1 to achieve 6. This systematic approach leads to 3x + 2y + 6.
Simplify: 2(3m + 5) - 4(m - 2)
2m + 10
2m - 18
2m + 18
6m + 18
Distribute the numbers to get 6m + 10 and -4m + 8, then combine the like terms to simplify to 2m + 18. This exercise reinforces proper distribution and combination of like terms.
Simplify: 2x + 3(x + 4)
3x + 12
5x + 12
2x + 12
5x + 4
First, distribute the 3 across (x + 4) to obtain 3x + 12, then add the term 2x. Combining the like terms gives the simplified answer 5x + 12.
Simplify: 6 - 2(1 - 3x)
4 - 6x
6 - 2x
6x - 4
6x + 4
Distribute -2 over (1 - 3x) to obtain -2 + 6x, then add the constant 6 to get 6x + 4. This problem highlights the need to carefully manage negative signs during distribution.
Simplify: 4(x + 2) - 3(x - 5)
7x - 7
x + 23
x + 7
7x + 23
Expand the expression to get 4x + 8 and -3x + 15. Combining like terms leads to x + 23, demonstrating proper application of the distributive property.
Combine like terms: 7b + 3 - 2b + 5 - b
6b + 8
7b + 5
4b - 8
4b + 8
Combine the b terms: 7b minus 2b minus b gives 4b, and add the constants 3 and 5 to get 8. The final simplified expression is 4b + 8.
Simplify: 2(3x - 4y + 5) - 3(2x - y - 2) + 4y
16 - y
-16 - y
16 + y
y - 16
Begin by distributing the factors within the parentheses and then combine the like terms. The x terms cancel out, the y terms combine to -y, and the constants add up to 16, resulting in 16 - y.
Simplify: 4(2x + 3) - 2(x - 5) + 3(x + 4)
7x + 34
9x + 12
9x + 38
9x + 34
Distribute each coefficient to eliminate the parentheses, then combine the x terms and constants separately. Detailed calculation shows the x terms sum to 9x and the constants to 34, yielding 9x + 34.
Simplify: 5(2y - 3) - 2(4y - 7) + (3y + 8)
7y - 5
5y + 7
5y - 7
7y + 5
First multiply to remove the parentheses, then add the coefficients of the y terms and the constants separately. This yields 5y from combining the variable terms and 7 from adding the constants, resulting in 5y + 7.
Simplify: 3(4m + 2) - 2(5m - 3) + m - 6
3m + 6
4m + 6
3m
3m - 6
Distribute the multipliers across the parentheses and then combine the like terms carefully. The m terms add up to 3m and the constant terms sum to 6, resulting in the simplified expression 3m + 6.
Simplify: 2(3x + 4) + 3(2x - 5) - 4(x - 6)
10x + 17
8x - 17
8x + 16
8x + 17
Start by distributing each term to remove the parentheses, then combine the like terms by adding the x coefficients and constants separately. The process results in 8x from the x terms and 17 from the constants, giving the simplified expression 8x + 17.
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Study Outcomes

  1. Identify like terms in algebraic expressions.
  2. Combine terms to simplify expressions effectively.
  3. Apply algebraic techniques to solve equations.
  4. Analyze problem-solving strategies for efficient term combination.
  5. Build confidence in tackling algebraic challenges for upcoming assessments.

Combining Like Terms Cheat Sheet

  1. Spot identical terms - Like terms are the superheroes of algebra because they share the exact same variables and exponents, allowing their coefficients to team up in arithmetic action. Think of 3x and -5x as teammates scoring a -2x goal, but remember 3x² and 3x just aren't on the same squad!
  2. Practice combining them - Grab your pen and practice pairing like terms to simplify expressions, such as turning 4x + 2x into a clean 6x. Regular drills will build your pattern‑recognition muscles and speed so those puzzles feel like a breeze.
  3. Combine constants too - Constants (numbers without variables) love to join the party too - 5 and -3 shaking hands become a mellow 2. Treat them exactly like variable terms and watch your expressions shrink.
  4. Use the distributive property - When parentheses crash the party, use the distributive property to expand before you combine, like turning 2(x + 3) into 2x + 6 for an easy team‑up. This extra step often reveals hidden like terms lurking inside.
  5. Handle negative signs - Watch your minus signs like secret ninjas - they flip who teams up with whom, since 3x - 2x gracefully surrenders to x. A tiny slip can change your entire answer, so edge‑proof your skills!
  6. Combine multiple variables - When variables multiply, like terms glamorously match both letters and exponents - 2xy + 3xy makes a fabulous 5xy. If you see xz and zx, swap them to check the match before combining!
  7. Check exponents exactly - Exponents are picky: x² doesn't buddy up with x³ or plain x. Always scan those little numbers to ensure a perfect exponent match before adding or subtracting.
  8. Simplify full expressions - Put on your detective hat and simplify longer expressions like 4x + 3x - 2 into a tidy 7x - 2. This habit not only clears clutter but also boosts confidence for tougher algebra mysteries!
  9. Reinforce with worksheets - Repetition is the secret sauce to mastery - grab extra worksheets to flex your combining muscles until you can do it in your sleep. Challenge yourself with timed drills to turn skills into reflexes.
  10. Master the fundamentals - Combining like terms is the bedrock of algebra, streamlining expressions and paving the way to solve equations like a pro. Master this early, and future math obstacles become much easier to hurdle!
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