Multiplying and FactoringALGEBRA 1 LESSON 9-2ALGEBRA 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

Multiplying and FactoringALGEBRA 1 LESSON 9-2ALGEBRA 1 LESSON 9-2

1. 3(302) = 906 2. 41(7) = 287 3. 9(504) = 4536

4. 4(6 + 5x) = 4(6) + 4(5x) = 24 + 20x

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

Solutions

9-2

Multiplying and FactoringALGEBRA 1 LESSON 9-2ALGEBRA 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 – 12g2 + 1 + 10g2 Multiply the coefficients and add the exponents of powers with the same base.

= –6g5 – 12g3 + 10g2 Simplify.

9-2

Multiplying and FactoringALGEBRA 1 LESSON 9-2ALGEBRA 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

Multiplying and FactoringALGEBRA 1 LESSON 9-2ALGEBRA 1 LESSON 9-2

Factor 4x3 + 12x2 – 16x.

Step 1: Find the GCF.

4x3 = 2 • 2 • x • x • x

12x2 = 2 • 2 • 3 • x • x

16x = 2 • 2 • 2 • 2 • x

Step 2: Factor out the GCF.

4x3 + 12x2 – 16x

= 4x(x2) + 4x(3x) + 4x(–4)

= 4x(x2 + 3x – 4)

The GCF is 2 • 2 • x, or 4x.

9-2

Multiplying and FactoringALGEBRA 1 LESSON 9-2ALGEBRA 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