EXAMPLE 3 Multiply polynomials vertically Find the product (b 2 + 6b – 7)(3b – 4). SOLUTION STEP 1 Multiply by – 4. b 2 + 6b – 7 – 4b 2 – 24b + 28 3b –

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EXAMPLE 3 Multiply polynomials vertically Find the product (b 2 + 6b – 7)(3b – 4). SOLUTION STEP 1 Multiply by – 4. b 2 + 6b – 7 – 4b 2 – 24b b – 4 STEP 2 Multiply by 3b. b 2 + 6b – 7 3b – 4 – 4b 2 – 24b b b 2 – 21b

Multiply polynomials vertically EXAMPLE 3 STEP 3 Add products. b 2 + 6b – 7 3b – 4 – 4b 2 – 24b b b 2 – 21b 3b b 2 – 45b + 28

Multiply polynomials horizontally EXAMPLE 4 Find the product (2x 2 + 5x – 1)(4x – 3). (2x 2 + 5x – 1)(4x – 3) Write product. = 2x 2 (4x – 3) + 5x(4x – 3) – 1(4x – 3) = 8x 3 – 6x x 2 – 15x – 4x + 3 Distributive property = 8x x 2 – 19x + 3 Combine like terms. FOIL PATTERN The letters of the word FOIL can help you to remember how to use the distributive property to multiply binomials. The letters should remind you of the words First, Outer, Inner, and Last.

Multiply polynomials horizontally EXAMPLE 4 (2x + 3)(4x + 1) First OuterInner Last = 8x 2 + 2x + 12x + 3

Multiply binomials using the FOIL pattern EXAMPLE 5 Find the product (3a + 4)(a – 2). (3a + 4)(a – 2) = (3a)(a) + (3a)(– 2) + (4)(a) + (4)(– 2) Write products of terms. = 3a 2 + (– 6a) + 4a + (– 8) Multiply. = 3a 2 – 2a – 8 Combine like terms.

GUIDED PRACTICE for Examples 3, 4, and 5 Find the product. SOLUTION STEP 1 Multiply by 2 x 2 + 2x + 1 2x 2 + 4x + 2 x + 2 STEP 2 Multiply by x x 2 + 2x + 1 x + 2 2x 2 + 4x + 2 (x 2 + 2x +1)(x + 2)4 x 3 + 2x 2 + x

GUIDED PRACTICE for Examples 3, 4, and 5 STEP 3 Add products. x 2 + 2x + 1 x + 2 2x 2 + 4x + 2 x 3 + 2x 2 + x x 3 + 4x 2 + 5x + 2

GUIDED PRACTICE for Examples 3, 4, and 5 Find the product. Write product. = 3y 2 (2y – 3) – y(2y – 3) + 5(2y – 3) = 6y 3 – 9y 2 – 2y 2 + 3y + 10y – 15 Distributive property = 6y 3 – 11y y – 15 Combine like terms. (3y 2 –y + 5)(2y – 3) SOLUTION (3y 2 –y + 5)(2y – 3) 5

GUIDED PRACTICE for Examples 3, 4, and 5 Find the product. SOLUTION (4b –5)(b – 2) 6 = (4b)(b) + (4b)(– 2) + (–5)(b) + (–5)(– 2) Write products of terms. = 4b 2 – 8b – 5b + 10 Multiply. = 4b 2 – 13b + 10 Combine like terms.