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Combining Like Terms practice questions

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Answer key with explanations

  1. Simplify 5c + 8c.

    Answer: 13c. Both terms have the variable part c, so add the coefficients: 5 + 8 = 13, and keep c. The answer 13c2 wrongly multiplies the letters, and 40c multiplies the coefficients.

  2. Which pair of terms are like terms?

    Answer: 6k and −k. Like terms have exactly the same variable part. 6k and −k both have the variable part k (the coefficients 6 and −1 may differ). 6 has no variable, 6k2 has k2, and 6j has the letter j.

  3. Simplify 9p − 4 − 5p + 10.

    Answer: 4p + 6. The p-terms: 9p − 5p = 4p. The constants: −4 + 10 = 6. So the result is 4p + 6. The answer 14p + 6 drops the minus sign on 5p, and 4p − 14 drops the sign on +10.

  4. Simplify 3w2 + 4w − 2w2 + w.

    Answer: w2 + 5w. The w2-terms: 3w2 − 2w2 = w2. The w-terms: 4w + w = 5w, because the lone w has coefficient 1. The w2 and w groups are not like terms, so they stay separate. The answer w2 + 4w forgets the coefficient 1, and 5w2 + 5w ignores the minus sign on 2w2.

  5. Simplify (3/4)n + (1/4)n − 2.

    Answer: n − 2. The n-terms share a denominator, so add the coefficients: 3/4 + 1/4 = 4/4 = 1, which gives 1n = n. The constant stays −2. The answer (1/2)n comes from adding the tops and the bottoms separately, and (3/16)n comes from multiplying the fractions.

  6. Simplify (8k + 3) − (5k − 6).

    Answer: 3k + 9. The minus sign flips both signs in the second group: −(5k − 6) = −5k + 6. So the expression is 8k + 3 − 5k + 6. The k-terms: 8k − 5k = 3k. The constants: 3 + 6 = 9. The answer 3k − 3 forgets to flip the sign of the −6.

  7. A triangle has side lengths 2m + 1, m + 4 and 3m − 2. Which expression gives its perimeter?

    Answer: 6m + 3. The perimeter is the sum of the three sides: (2m + 1) + (m + 4) + (3m − 2). The m-terms: 2m + m + 3m = 6m. The constants: 1 + 4 − 2 = 3. So the perimeter is 6m + 3. The answer 5m + 3 forgets the coefficient 1 on the middle m.

  8. Maya simplified 4z − 9 + z + 6 and got 4z − 3. What went wrong?

    Answer: She forgot that the lone z means 1z. The correct answer is 5z − 3.. The z-terms are 4z and 1z, so they combine to 5z. The constants −9 + 6 = −3 were right, but the z part was wrong. A test number shows it: at z = 3 the original is 12 − 9 + 3 + 6 = 12, but 4z − 3 = 9, while 5z − 3 = 12.

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