EXAMPLE 3 Multiply polynomials vertically

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EXAMPLE 3 Multiply polynomials vertically Find the product (b2 + 6b – 7)(3b – 4). SOLUTION STEP 1 Multiply by – 4. STEP 2 Multiply by 3b. b2 + 6b – 7 b2 + 6b – 7 3b – 4 3b – 4 – 4b2 – 24b + 28 – 4b2 – 24b + 28 3b3 + 18b2 – 21b

EXAMPLE 3 Multiply polynomials vertically STEP 3 Add products. b2 + 6b – 7 3b – 4 – 4b2 – 24b + 28 3b3 + 18b2 – 21b 3b3 + 14b2 – 45b + 28

Multiply polynomials horizontally EXAMPLE 4 Multiply polynomials horizontally Find the product (2x2 + 5x – 1)(4x – 3). (2x2 + 5x – 1)(4x – 3) Write product. = 2x2(4x – 3) + 5x(4x – 3) – 1(4x – 3) Distributive property = 8x3 – 6x2 + 20x2 – 15x – 4x + 3 Distributive property = 8x3 + 14x2 – 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.

EXAMPLE 4 Multiply polynomials horizontally First Outer Inner Last (2x + 3)(4x + 1) = 8x2 + 2x + 12x + 3

Multiply binomials using the FOIL pattern EXAMPLE 5 Multiply binomials using the FOIL pattern Find the product (3a + 4)(a – 2). (3a + 4)(a – 2) = (3a)(a) + (3a)(– 2) + (4)(a) + (4)(– 2) Write products of terms. = 3a2 + (– 6a) + 4a + (– 8) Multiply. = 3a2 – 2a – 8 Combine like terms.

GUIDED PRACTICE for Examples 3, 4, and 5 Find the product. (x2 + 2x +1)(x + 2) 4. x3 + 4x2 + 5x + 2 ANSWER 5. (3y2 –y + 5)(2y – 3) ANSWER 6y3 – 11y2 + 13y – 15 6. (4b –5)(b – 2) ANSWER 4b2 – 13b + 10