1. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 1 Exponents and Polynomials 5

2. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 2 1.Multiply a monomial and a polynomial. 2.Multiply two polynomials. 3.Multiply binomials by the FOIL method. Objectives 5.3 Multiplying Polynomials

3. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 3 Multiply 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.

4. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 4 Multiply 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

5. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 5 Multiply 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.

6. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 6 Multiply 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

7. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 7 5n + 8n – 3n – 2 32 Multiply 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

8. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 8 Multiply Binomials by the FOIL Method 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.

9. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 9 Multiply 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:

10. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 10 Multiply 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

11. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 11 Multiply 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

12. Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 12 Multiply 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