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**Multiplying and Factoring**

ALGEBRA 1 LESSON 9-2 (For help, go to Lesson 1–7.) Multiply. 1. 3(302) 2. 41(7) 3. 9(504) Simplify each expression. 4. 4(6 + 5x) 5. –8(2y + 1) 6. (5v – 1)5 7. 7(p – 2) 8. (6 – x)9 9. –2(4q – 1) 9-2

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**Multiplying and Factoring**

ALGEBRA 1 LESSON 9-2 Solutions 1. 3(302) = (7) = (504) = 4536 4. 4(6 + 5x) = 4(6) + 4(5x) = x 5. –8(2y + 1) = (–8)(2y) + (–8)(1) = –16y – 8 6. (5v – 1)5 = (5v)(5) – (1)(5) = 25v – 5 7. 7(p – 2) = 7p – 7(2) = 7p – 14 8. (6 – x)9 = 6(9) – 9x = 54 – 9x 9. –2(4q – 1) = (–2)(4q) – (–2)(1) = –8q + 2 9-2

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**Multiplying and Factoring**

ALGEBRA 1 LESSON 9-2 Simplify –2g2(3g3 + 6g – 5). –2g2(3g3 + 6g – 5) = –2g2(3g3) –2g2(6g) –2g2(–5) Use the Distributive Property. = –6g2 + 3 – 12g g2 Multiply the coefficients and add the exponents of powers with the same base. = –6g5 – 12g3 + 10g2 Simplify. 9-2

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**Multiplying and Factoring**

ALGEBRA 1 LESSON 9-2 Find the GCF of 2x4 + 10x2 – 6x. List the prime factors of each term. Identify the factors common to all terms. 2x4 = 2 • x • x • x • x 10x2 = 2 • 5 • x • x 6x = 2 • 3 • x The GCF is 2 • x, or 2x. 9-2

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**Multiplying and Factoring**

ALGEBRA 1 LESSON 9-2 Factor 4x3 + 12x2 – 16x. Step 1: Find the GCF. Step 2: Factor out the GCF. 4x3 + 12x2 – 16x 4x3 = 2 • 2 • x • x • x 12x2 = 2 • 2 • 3 • x • x 16x = 2 • 2 • 2 • 2 • x = 4x(x2) + 4x(3x) + 4x(–4) = 4x(x2 + 3x – 4) The GCF is 2 • 2 • x, or 4x. 9-2

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**Multiplying and Factoring**

ALGEBRA 1 LESSON 9-2 1. Simplify –2x2(–3x2 + 2x + 8). 2. Find the GCF of 16b4 – 4b3 + 8b2. 3. Factor 3x3 + 9x2. 4. Factor 10y3 + 5y2 – 15y. 6x4 – 4x3 – 16x2 4b2 3x2(x + 3) 5y(2y + 3)(y – 1) 9-2

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