EXAMPLE 4 a Simplify by combining like terms

EXAMPLE 4 a. Simplify by combining like terms Distributive property 8 x + 3 x = (8 + 3)x = 11 x b. Add coefficients. 5 p 2 + p – 2 p 2 = (5 p 2 – 2 p 2) + p = 3 p 2 + p c. Group like terms. Combine like terms. 3(y + 2) – 4(y – 7) = 3 y + 6 – 4 y + 28 Distributive property = (3 y – 4 y) + (6 + 28) Group like terms. = –y + 34 Combine like terms.

EXAMPLE 4 d. Simplify by combining like terms 2 x – 3 y – 9 x + y = (2 x – 9 x) + (– 3 y + y) Group like terms. = – 7 x – 2 y Combine like terms.

GUIDED PRACTICE for Example 5 8. Identify the terms, coefficients, like terms, and constant terms in the expression 2 + 5 x – 6 x 2 + 7 x – 3. Then simplify the expression. SOLUTION Terms: 2, 5 x, – 6 x 2 , 7 x, – 3 5 from 5 x, – 6 from – 6 x 2 , 7 from 7 x Coefficients: 5 x and 7 x, 2 and – 3 Like terms: 2 and – 3 Constants: Simplify: State the problem. 2 + 5 x – 6 x 2 + 7 x – 3 = – 6 x 2 + 5 x + 7 x – 3 + 2 Group like terms. = – 6 x 2 +12 x – 1 Combine like terms.

for Example 5 GUIDED PRACTICE Simplify the expression. 9. 15 m – 9 m SOLUTION 15 m – 9 m = 6 m 10. Combine like terms. 2 n – 1 + 6 n + 5 SOLUTION 2 n – 1 + 6 n + 5 = 2 n + 6 n + 5 – 1 = 8 n + 4 Group like terms. Combine like terms.

for Example 5 GUIDED PRACTICE 11. 3 p 3 + 5 p 2 – p 3 SOLUTION 3 p 3 + 5 p 2 – p 3 = 3 p 3 – p 3 + 5 p 2 = 2 p 3 + 5 p 3 12. Group like terms. Combine like terms. 2 q 2 + q – 7 q – 5 q 2 SOLUTION 2 q 2 + q – 7 q – 5 q 2 = 2 q 2 – 5 q 2 – 7 q + q = – 3 q 2 – 6 q Group like terms. Combine like terms.

for Example 5 GUIDED PRACTICE 13. 8(x – 3) – 2(x + 6) SOLUTION 8(x – 3) – 2(x + 6) = 8 x – 24 – 2 x – 12 = 8 x – 24 – 12 = 6 x – 36 14. Distributive property Group like terms. Combine like terms. – 4 y – x + 10 x + y SOLUTION – 4 y – x + 10 x + y = – 4 y + y – x + 10 x = 9 x – 3 y Group like terms. Combine like terms.