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Quizzes > High School Quizzes > Mathematics

Combining Like Terms Practice Quiz

Master algebra simplification with engaging practice problems

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a challenging high school math trivia quiz.

Simplify: 3x + 2x
5x
6x
x
5
Combining the like terms 3x and 2x gives 5x because you add the coefficients. The variable remains unchanged.
Simplify: 7y - 4y
3y
11y
7y
4y
Subtracting the coefficients of like terms, 7y minus 4y equals 3y. The variable y stays the same during the process.
Simplify: 5a + 3b - 2a
3a + 3b
7a + 3b
3a
5a - 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
4x + 2
4x
3x + 2
2x + 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
7 - 3y
7 + 3y
10 - 3y
7y - 3
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
2x + 10
6x + 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 + 2b + 4c
11a + 4c
5a - 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
11x + 8
10x + 8
11x + 4
8x + 11
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)
2y - 11
2y - 15
6y - 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 + 2y + 6
3x + 2y + 8
7x + 6
3x + 3y + 6
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 + 18
2m + 10
6m + 18
2m - 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)
5x + 12
5x + 4
2x + 12
3x + 12
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)
6x + 4
4 - 6x
6x - 4
6 - 2x
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)
x + 23
7x - 7
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
4b + 8
6b + 8
4b - 8
7b + 5
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
y - 16
-16 - y
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)
9x + 34
9x + 12
7x + 34
9x + 38
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)
5y + 7
5y - 7
7y + 5
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
3m - 6
4m + 6
3m
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)
8x + 17
8x - 17
10x + 17
8x + 16
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! Combining Like Terms Worksheet - GeeksforGeeks
  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. A Free Printable Combining Like Terms Worksheet
  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. Combining Like Terms Worksheet - GeeksforGeeks
  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. How to Combine Like Terms? (+FREE Worksheet!)
  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! Combining Like Terms and Solving | EdBoost
  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! A Free Printable Combining Like Terms Worksheet
  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. Combining Like Terms Worksheet - GeeksforGeeks
  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! Combining Like Terms Practice Problems | Math = Love
  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. A Free Printable Combining Like Terms Worksheet
  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! How to Combine Like Terms? (+FREE Worksheet!)
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