EXAMPLE 1 Multiply a monomial and a polynomial Find the product 2x 3 (x 3 + 3x 2 – 2x + 5). 2x 3 (x 3 + 3x 2 – 2x + 5) Write product. = 2x 3 (x 3 ) + 2x.

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EXAMPLE 1 Multiply a monomial and a polynomial Find the product 2x 3 (x 3 + 3x 2 – 2x + 5). 2x 3 (x 3 + 3x 2 – 2x + 5) Write product. = 2x 3 (x 3 ) + 2x 3 (3x 2 ) – 2x 3 (2x) + 2x 3 (5) Distributive property = 2x 6 + 6x 5 – 4x x 3 Product of powers property

Multiply polynomials using a table EXAMPLE 2 Find the product (x – 4)(3x + 2). STEP 1 Write subtraction as addition in each polynomial. (x – 4)(3x + 2) = [x + (– 4)](3x + 2) SOLUTION

Multiply polynomials using a table EXAMPLE 2 ANSWER The product is 3x 2 + 2x – 12x – 8, or 3x 2 – 10x – 8. 3x23x2 x – 4 3x3x 2 – 8– 12x 2x2x3x23x2 x – 4 3x3x 2 STEP 2 Make a table of products.

GUIDED PRACTICE for Examples 1 and 2 Find the product. 1. x(7x 2 +4) ANSWER 7x 3 + 4x 2. (a +3)(2a +1) ANSWER 2a 2 + 7a (4n – 1)(n + 5) ANSWER 4n n – 5