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EXAMPLE 1 Apply the distributive property Use the distributive property to write an equivalent expression. a. 4(y + 3) = 4y + 12 b. (y + 7)y = y2 + 7y c. n(n – 9) = n2 – 9n d. (2 – n)8 = 16 – 8n

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**Distribute a negative number**

EXAMPLE 2 Distribute a negative number Use the distributive property to write an equivalent expression. a. –2(x + 7)= – 2(x) + – 2(7) Distribute – 2. = – 2x – 14 Simplify. b. (5 – y)(–3y) = 5(–3y) – y(–3y) Distribute – 3y. = – 15y + 3y2 Simplify.

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**Distribute a negative number**

EXAMPLE 2 Distribute a negative number c. –(2x – 11) = (–1)(2x – 11) of – 1 Multiplicative property = (– 1)(2x) – (–1)(11) Distribute – 1. = – 2x + 11 Simplify.

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EXAMPLE 3 Identify parts of an expression Identify the terms, like terms, coefficients, and constant terms of the expression 3x – 4 – 6x + 2. SOLUTION Write the expression as a sum: 3x + (–4) + (–6x) + 2 Terms: 3x, – 4, – 6x, 2 Like terms: 3x and – 6x; – 4 and 2 Coefficients: 3, – 6 Constant terms: – 4, 2

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GUIDED PRACTICE for Examples 1, 2 and 3 Use the distributive property to write an equivalent expression. (x + 3) = 2x + 6 2. – (4 – y) = – 4 + y 3. (m – 5)(– 3m) = – 3m2 + 15m 4. (2n + 6) 1 2 = n + 3

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GUIDED PRACTICE for Examples 1, 2 and 3 Identify the terms, like terms, coefficients, and constant terms of the expression – 7y + 8 – 6y – 13. Terms: – 7y, 8, – 6y, – 13 ANSWER Like terms: – 7y and – 6y , 8 and – 13; Coefficients: – 7, – 6 Constant terms: 8, – 13

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