1. Holt McDougal Algebra 2 Multiplying Polynomials Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers. Objectives

2. Holt McDougal Algebra 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 )

3. Holt McDougal Algebra 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 McDougal Algebra 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 McDougal Algebra 2 Multiplying Polynomials Find the product. Example 2A: Multiplying Polynomials (a – 3)(2 – 5a + a 2 )

6. Holt McDougal Algebra 2 Multiplying Polynomials (a – 3)(2 – 5a + a 2 ) Find the product. Example 2A: Multiplying Polynomials

7. Holt McDougal Algebra 2 Multiplying Polynomials (y 2 – 7y + 5)(y 2 – y – 3) Find the product. Example 2B: Multiplying Polynomials

8. Holt McDougal Algebra 2 Multiplying Polynomials Check It Out! Example 2a Find the product. (3b – 2c)(3b 2 – bc – 2c 2 )

9. Holt McDougal Algebra 2 Multiplying Polynomials (x 2 – 4x + 1)(x 2 + 5x – 2) Find the product. Check It Out! Example 2b

10. Holt McDougal Algebra 2 Multiplying Polynomials Example 3: Business Application A standard Burly Box is p ft by 3p ft by 4p ft. A large Burly Box has 1.5 ft added to each dimension. Write a polynomial V(p) in standard form that can be used to find the volume of a large Burly Box.

11. Holt McDougal Algebra 2 Multiplying Polynomials Check It Out! Example 3 Mr. Silva manages a manufacturing plant. From 1990 through 2005 the number of units produced (in thousands) can be modeled by N(x) = 0.02x 2 + 0.2x + 3. The average cost per unit (in dollars) can be modeled by C(x) = –0.004x 2 – 0.1x + 3. Write a polynomial T(x) that can be used to model the total costs.

12. Holt McDougal Algebra 2 Multiplying Polynomials Example 4: Expanding a Power of a Binomial Find the product. (a + 2b) 3

13. Holt McDougal Algebra 2 Multiplying Polynomials Check It Out! Example 4a Find the product. (x + 4) 4

14. Holt McDougal Algebra 2 Multiplying Polynomials Check It Out! Example 4b Find the product. (2x – 1) 3

15. Holt McDougal Algebra 2 Multiplying Polynomials Example 5: Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. A. (k – 5) 3

16. Holt McDougal Algebra 2 Multiplying Polynomials Example 5: Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. B. (6m – 8) 3

17. Holt McDougal Algebra 2 Multiplying Polynomials Check It Out! Example 5 Expand each expression. a. (x + 2) 3 b. (x – 4) 5

18. Holt McDougal Algebra 2 Multiplying Polynomials Check It Out! Example 5 c. (3x + 1) 4 Expand the expression.

19. Holt McDougal Algebra 2 Multiplying Polynomials 4. Find the product. (y – 5) 4 Lesson Quiz 2. (2a 3 – a + 3)(a 2 + 3a – 5) 1. 5jk(k – 2j) 3. The number of items is modeled by 0.3x 2 + 0.1x + 2, and the cost per item is modeled by g(x) = –0.1x 2 – 0.3x + 5. Write a polynomial c(x) that can be used to model the total cost. Find each product. 5. Expand the expression. (3a – b) 3