➕ Algebra 1 · Equations

Combining Like Terms: true or false

Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.

All statements and answers

• 7q + 2q = 9q.

  ✓ True. Add the coefficients, 7 + 2 = 9, and keep the variable part q.

• 4k + 3k = 7k².

  ✗ False. Adding counts how many k’s you have, so 4k + 3k = 7k. Adding never changes the exponent. Multiplying can: 4k × 3k = 12k².

• 5n + 2 simplifies to 7n.

  ✗ False. 5n has a variable and 2 is a constant, so they are not like terms. The expression 5n + 2 is already as simple as it gets.

• −3p + 8p = 5p.

  ✓ True. The coefficients combine as −3 + 8 = 5.

• 6w − w = 6.

  ✗ False. A lone w means 1w, so 6w − 1w = 5w.

• r² and 3r² are like terms.

  ✓ True. Both have the variable part r². Their coefficients, 1 and 3, can be different. Combined: 4r².

• 2fg and 2f are like terms because both contain an f.

  ✗ False. Like terms need the same whole variable part. The variable part of 2fg is fg, but the variable part of 2f is f.

• (5z + 4) − (z + 1) simplifies to 4z + 3.

  ✓ True. Remove the parentheses, flipping the signs of the second group: 5z + 4 − z − 1. Then 5z − z = 4z and 4 − 1 = 3.

• 10 − (2k + 3) equals 7 + 2k.

  ✗ False. The minus sign flips both terms in the group: 10 − 2k − 3 = 7 − 2k.

• The constants 5 and −9 are like terms.

  ✓ True. Constants have no variable part, so they are like terms with each other. 5 + (−9) = −4.

• 4p and 4q are like terms because both have the coefficient 4.

  ✗ False. Like terms need the same variable part, not the same coefficient. p and q are different letters.

• 8 + 3m − 5 and 3m + 3 have the same value for every number m.

  ✓ True. The constants combine: 8 − 5 = 3. So 8 + 3m − 5 = 3m + 3 for every m.