1. Holt Algebra 2 6-2 Multiplying Polynomials Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers. Objectives To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.

2. Holt Algebra 2 6-2 Multiplying Polynomials Find each product. Example 1: Multiplying a Monomial and a Polynomial A. 4y 2 (y 2 + 3) B. fg(f 4 + 2f 3 g – 3f 2 g 2 + fg 3 ) 4y 2  y 2 + 4y 2  3 4y 2 (y 2 + 3) 4y 4 + 12y 2 fg(f 4 + 2f 3 g – 3f 2 g 2 + fg 3 ) fg  f 4 + fg  2f 3 g – fg  3f 2 g 2 + fg  fg 3 f 5 g + 2f 4 g 2 – 3f 3 g 3 + f 2 g 4

3. Holt Algebra 2 6-2 Multiplying Polynomials Check It Out! Example 1 Find each product. a. 3cd 2 (4c 2 d – 6cd + 14cd 2 ) b. x 2 y(6y 3 + y 2 – 28y + 30)

4. Holt Algebra 2 6-2 Multiplying Polynomials To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first. Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified.

5. Holt Algebra 2 6-2 Multiplying Polynomials Find the product. Example 2A: Multiplying Polynomials (a – 3)(2 – 5a + a 2 ) a(a 2 ) + a(–5a) + a(2) – 3(a 2 ) – 3(–5a) –3(2) Method 1 Multiply horizontally. a 3 – 5a 2 + 2a – 3a 2 + 15a – 6 a 3 – 8a 2 + 17a – 6 (a – 3)(a 2 – 5a + 2)

6. Holt Algebra 2 6-2 Multiplying Polynomials (a – 3)(2 – 5a + a 2 ) Find the product. Example 2A: Multiplying Polynomials Method 2 Multiply vertically. a 2 – 5a + 2 a – 3 – 3a 2 + 15a – 6 a 3 – 5a 2 + 2a a 3 – 8a 2 + 17a – 6

7. Holt Algebra 2 6-2 Multiplying Polynomials Check It Out! Example 2a Find the product. (3b – 2c)(3b 2 – bc – 2c 2 ) Multiply horizontally.

8. Holt Algebra 2 6-2 Multiplying Polynomials (x 2 – 4x + 1)(x 2 + 5x – 2) Find the product. Check It Out! Example 2b Multiply vertically

9. Holt Algebra 2 6-2 Multiplying Polynomials Find the product.(a + 2b) 3

10. Holt Algebra 2 6-2 Multiplying Polynomials Find the product.(x + 4) 4

11. Holt Algebra 2 6-2 Multiplying Polynomials Find the product.(2x – 1) 3

12. Holt Algebra 2 6-2 Multiplying Polynomials Lesson Quiz 2. (2a 3 – a + 3)(a 2 + 3a – 5) 5jk 2 – 10j 2 k 1. 5jk(k – 2j) 2a 5 + 6a 4 – 11a 3 + 14a – 15 Find each product. 3. (3a – b) 3 27a 3 – 27a 2 b + 9ab 2 – b 3