1. EXAMPLE 3 Multiply polynomials vertically and horizontally a. Multiply – 2y 2 + 3y – 6 and y – 2 in a vertical format. b. Multiply x + 3 and 3x 2 – 2x + 4 in a horizontal format. SOLUTION a. – 2y 2 + 3y – 6 y – 2 4y 2 – 6y + 12 Multiply – 2y 2 + 3y – 6 by – 2. – 2y 3 + 3y 2 – 6y Multiply – 2y 2 + 3y – 6 by y – 2y 3 +7y 2 –12y + 12 Combine like terms.

2. EXAMPLE 3 Multiply polynomials vertically and horizontally b. (x + 3)(3x 2 – 2x + 4) = (x + 3)3x 2 – (x + 3)2x + (x + 3)4 = 3x 3 + 9x 2 – 2x 2 – 6x + 4x + 12 = 3x 3 + 7x 2 – 2x + 12

3. EXAMPLE 4 Multiply three binomials Multiply x – 5, x + 1, and x + 3 in a horizontal format. (x – 5)(x + 1)(x + 3) = (x 2 – 4x – 5)(x + 3) = (x 2 – 4x – 5)x + (x 2 – 4x – 5)3 = x 3 – 4x 2 – 5x + 3x 2 – 12x – 15 = x 3 – x 2 – 17x – 15

4. EXAMPLE 5 Use special product patterns a. (3t + 4)(3t – 4) Sum and difference = 9t 2 – 16 b. (8x – 3) 2 Square of a binomial = 64x 2 – 48x + 9 c. (pq + 5) 3 Cube of a binomial = p 3 q 3 + 15p 2 q 2 + 75pq + 125 = (3t) 2 – 4 2 = (8x) 2 – 2(8x)(3) + 3 2 = (pq) 3 + 3(pq) 2 (5) + 3(pq)(5) 2 + 5 3

5. GUIDED PRACTICE for Examples 3, 4 and 5 Find the product. 3. (x + 2)(3x 2 – x – 5) SOLUTION 3x 2 – x – 5 x + 2 6x 2 – 2x – 10 3x 3 – x 2 – 5x 3x 3 + 5x 2 – 7x – 10 Multiply 3x 2 – x – 5 by 2. Multiply 3x 2 – x – 5 by x. Combine like terms.

6. GUIDED PRACTICE for Examples 3, 4 and 5 4. (a – 5)(a + 2)(a + 6) SOLUTION (a – 5)(a + 2)(a + 6) = (a 2 – 3a – 10)(a + 6) = (a 2 – 3a – 10)a + (a 2 – 3a – 10)6 = (a 3 – 3a 2 – 10a + 6a 2 – 18a – 60) = (a 3 + 3a 2 – 28a – 60)

7. GUIDED PRACTICE for Examples 3, 4 and 5 5. (xy – 4) 3 SOLUTION (xy – 4) 3 = (xy) 3 – 3(xy) 2 + 3(xy)(4) 2 – (4) 3 = x 3 y 3 – 12x 2 y 2 + 48xy – 64