1. 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

2. 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

3. 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

4. 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

5. 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

6. 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