13 Exponents and Polynomials.

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Presentation transcript:

13 Exponents and Polynomials

13.3 Multiplying Polynomials Objectives 1. Multiply a monomial and a polynomial. 2. Multiply two polynomials. 3. Multiply binomials by the FOIL method.

Multiply a Monomial and a Polynomial Example 1 Find each product. (a) 5x ( 6x + 7 ) 2 4 = 5x ( 6x ) 2 4 + 5x ( 7 ) 2 Distributive property = 30x + 35x 6 2 Multiply monomials.

Multiply a Monomial and a Polynomial Example 1 (concluded) Find each product. (b) – 2h ( – 3h + 8h – 1 ) 4 9 2 Distributive property = – 2h (– 3h ) 4 9 + (– 2h ) (8h ) 4 2 + (– 2h )(– 1) 4 = 6h 13 – 16h 6 + 2h 4 Multiply monomials.

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.

Multiply Two Polynomials Example 2 ( 2y – 5 ) ( 2y – 7y + 4 ) 2 3 Distributive property = (2y ) 2 3 (–7y) (2y ) 2 + (4) (2y ) 2 + (–5) (2y ) 3 + (–7y) + (–5) (4) + (–5) = 4y 5 14y 3 – 8y 2 + – 10y 3 + 35y – 20 = 4y 5 24y 3 – 8y 2 + 35y – 20 Combine like terms.

Multiply Two Polynomials Example 3 5n + 8n – 3n – 2 3 2 4n + 3 2 15n 3 + 24n 2 – 9n – 6 20n 5 + 32n 4 – 12n 3 – 8n 2 20n 5 + 32n 4 + 3n 3 + 16n 2 – 9n – 6

Multiply Binomials by the FOIL Method Multiplying Binomials by the FOIL Method Step 1 Multiply the two First terms of the binomials to get the first term of the answer. Step 2 Find the Outer product and the Inner product and add them (when possible) to get the middle term of the answer. Step 3 Multiply the two Last terms of the binomials to get the last term of the answer.

Multiply Binomials by the FOIL Method Example 4 F O I L = 3y – 2y – 12y + 8 2 ( y – 4 ) ( 3y – 2 ) = 3y – 14y + 8 2 Multiply the first terms: y ( 3y ) F Multiply the outer terms: y ( – 2 ) O Multiply the inner terms: – 4 ( 3y ) I Multiply the last terms: – 4 (– 2 ) L

Multiply Binomials by the FOIL Method Example 5 F O I L = 5n + n – 35n – 7 2 ( n – 7 ) ( 5n + 1 ) = 5n – 34n – 7 2 Multiply the first terms: n ( 5n ) F Multiply the outer terms: n ( 1 ) O Multiply the inner terms: – 7 ( 5n ) I Multiply the last terms: – 7 ( 1 ) L

Multiply Binomials by the FOIL Method Example F O I L = 27g – 12g + 18g – 8 2 ( 3g + 2 ) ( 9g – 4 ) = 27g + 6g – 8 2 Multiply the first terms: 3g ( 9g ) F Multiply the outer terms: 3g ( – 4 ) O Multiply the inner terms: 2 ( 9g ) I Multiply the last terms: 2 ( – 4 ) L

Multiply Binomials by the FOIL Method Example 6 F O I L = 24a – 12ab + 12ab – 6b 2 ( 6a + 3b ) ( 4a – 2b ) = 24a – 6b 2 Multiply the first terms: 6a ( 4a ) F Multiply the outer terms: 6a ( – 2b ) O Multiply the inner terms: 3b ( 4a ) I Multiply the last terms: 3b ( – 2b ) L