1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 2 Exponents and Polynomials Chapter 5

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 3 5.3 Multiplying Polynomials

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 4 5.3 Multiplying Polynomials Objectives 1.Multiply a monomial and a polynomial. 2.Multiply two polynomials. 3.Multiply binomials by the FOIL method.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 5 5.3 Multiplying Polynomials Multiplying a Monomial and a Polynomial (a) 5x ( 6x + 7 ) 24 Distributive property = 5x ( 6x ) 24 +5x ( 7 ) 2 = 30x + 35x 62 Multiply monomials. Example 1 Find each product.

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 6 5.3 Multiplying Polynomials Multiplying a Monomial and a Polynomial Distributive property = – 2h (– 3h ) 49 (b) – 2h ( – 3h + 8h – 1 ) 492 + (– 2h ) (8h ) 42 + (– 2h )(– 1) 4 Example 1 (concluded) Find each product. Multiply monomials. = 6h 13 – 16h 6 + 2h 4

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 7 5.3 Multiplying Polynomials Multiplying Two Polynomials Multiplying Polynomials To multiply two polynomials, multiply each term of the second polynomial by each term of the first polynomial and add the products.

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 8 5.3 Multiplying Polynomials Multiplying Two Polynomials Distributive property ( 2y – 5 ) ( 2y – 7y + 4 ) 2 3 = (2y ) 2 3 (–7y) (2y ) 2 + (4) (2y ) 2 + (–7y) + (–5)(4) + (–5) (2y ) 3 + = 4y4y 5 14y 3 – 8y8y 2 + – 20 + 35y – 10y 3 = 4y4y 5 24y 3 – 8y8y 2 ++ 35y– 20 Combine like terms. Example 2

9. 5n + 8n – 3n – 2 32 Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 9 5.3 Multiplying Polynomials Multiplying Two Polynomials 4n + 3 2 – 6– 9n + 24n 2 15n 3 – 8n 2 – 12n 3 + 32n 4 20n 5 – 6– 9n + 3n 3 + 32n 4 20n 5 + 16n 2 Example 3

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 10 5.3 Multiplying Polynomials Multiplying Binomials by the FOIL Method Step 1Multiply the two First terms of the binomials to get the first term of the answer. Step 2Find the Outer product and the Inner product and add them (when possible) to get the middle term of the answer. Step 3Multiply the two Last terms of the binomials to get the last term of the answer.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 11 5.3 Multiplying Polynomials Multiplying Binomials by the FOIL Method F ( y – 4 ) ( 3y – 2 ) O I L y ( 3y ) y ( – 2 ) – 4 ( 3y ) – 4 (– 2 ) = 3y – 2y – 12y + 8 2 = 3y – 14y + 8 2 FOIL Example 4 Multiply the last terms: Multiply the inner terms: Multiply the outer terms: Multiply the first terms:

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 12 5.3 Multiplying Polynomials Multiplying Binomials by the FOIL Method F ( n – 7 ) ( 5n + 1 ) O I L n ( 5n )Multiply the first terms: n ( 1 )Multiply the outer terms: – 7 ( 5n )Multiply the inner terms: – 7 ( 1 )Multiply the last terms: = 5n + n – 35n – 7 2 = 5n – 34n – 7 2 FOIL Example 5

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 13 5.3 Multiplying Polynomials Multiplying Binomials by the FOIL Method F ( 3g + 2 ) ( 9g – 4 ) O I L 3g ( 9g )Multiply the first terms: 3g ( – 4 )Multiply the outer terms: 2 ( 9g )Multiply the inner terms: 2 ( – 4 )Multiply the last terms: = 27g – 12g + 18g – 8 2 = 27g + 6g – 8 2 FOIL Example 6

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 14 5.3 Multiplying Polynomials Multiplying Binomials by the FOIL Method F ( 6a + 3b ) ( 4a – 2b ) O I L 6a ( 4a )Multiply the first terms: 6a ( – 2b )Multiply the outer terms: 3b ( 4a )Multiply the inner terms: 3b ( – 2b )Multiply the last terms: FOIL = 24a – 12ab + 12ab – 6b 2 2 = 24a – 6b 2 2 Example 6 (cont.)