Combining Like Terms

1. EXAMPLE 1 Combining Like Terms Simplify the expression 7c+ 9 – 3c. 7c + 9 – 3c = 7c + 9 + (–3c) Write expression as a sum. Commutative property of addition = 7c + (–3c) + 9 = [7 + (–3)] c + 9 Distributive property = 4c+ 9 Simplify.

2. EXAMPLE 2 Coefficients, Constant Terms, and Like Terms Identify the coefficients, constant terms, and like terms of the expression x+4–2x–10. First, write the expression as a sum:x+ 4 + (–2x) + (–10). x+ 4 + (–2x) + (–10)

3. EXAMPLE 3 Simplifying an Expression Simplify the expression 5(w – 4) + w + 8. 5(w – 4) + w + 8 = 5w – 20 + w + 8 Distributive property = 5w + (–20) + w+8 Write as a sum. = 5w + w + (–20) + 8 Commutative property = 6w + (–12) Combine like terms. = 6w– 12 Rewrite without parentheses.

4. coefficients: –3, 4; constant term: 1; like terms: –3z, 4z; z +1 coefficients: –9, 7; constant terms: 15, –6; like terms: –9r, 7r and 15, –6; –2r +9 coefficients: 2, –2; constant terms: 8, –4; like terms: 2y, –2y and 8, –4; 4 ANSWER ANSWER ANSWER GUIDED PRACTICE for Examples 1, 2, and 3 Identify the coefficients, constant term(s), and like terms of the expression. Then simplify the expression. 1. –3z + 1 + 4z 2. 15 – 9r+ 7r– 6 3. 2y + 8 – 2y – 4

5. coefficients: –8, 9; constant terms: 16, –8; like terms: –8k, 9k and 16, –8; k + 8 coefficients: 6, –6; constant terms: –18, –1; like terms: 6a, –6a and –18, –1; –19 coefficients: –7, 2; constant term: 5; like terms: –7m, 2m; –5m + 5 ANSWER ANSWER ANSWER GUIDED PRACTICE for Examples 1, 2, and 3 Identify the coefficients, constant term(s), and like terms of the expression. Then simplify the expression. 4. 16 – 8k + 9k– 8 5. 6a– 18 – 1 – 6a 6. –7m + 5 + 2m