2.2-Multiply Polynomials a3 + a3 = 2a3 b4(b3) = b4+3 = b7 Area = length * width Volume = length * width * height MEMORIZE!!

=5x4(2x3) – 5x4(3x2) + 5x4(x) –5x4(6) =10x7 – 15x6 + 5x5 – 30x4 Find the product 5x4(2x3 - 3x2 + x - 6) =5x4(2x3) – 5x4(3x2) + 5x4(x) –5x4(6) =10x7 – 15x6 + 5x5 – 30x4

Multiply polynomials horizontally Find the product (9x2 – x + 6)(5x – 2) =9x2(5x – 2) – x(5x – 2) + 6(5x – 2) =45x3 – 18x2 – 5x2 + 2x + 30x – 12 =45x3 – 23x2 + 32x - 12

(2x - 1)(7x + 6) =14x2 + 12x + (-7x) + (-6) =14x2 + 5x - 6 Multiply Binomials Find the product (2x - 1)(7x + 6) =(2x)(7x) + (2x)(6) + (-1)(7x) + (-1)(6) =14x2 + 12x + (-7x) + (-6) =14x2 + 5x - 6

Write a polynomial for the area of the figure Area = L * W = (3x + 1)(x + 2) = 3x2 + 6x + x + 2 = 3x2 + 7x + 2

Write the polynomial for the volume of the rectangular prism Volume = L * W * H = x(x + 1)(x + 2) = x[(x)(x) + (x)(2) + (1)(x) + (1)(2)] = x(x2 + 2x + x + 2) = x(x2 + 3x + 2) = x(x2) + x(3x) + x(2) = x3 + 3x2 + 2x

-5m3(4m4 – 3m + 1) = -5m3(4m4) – 5m3(-3m) - 5m3(1) Examples -5m3(4m4 – 3m + 1) = -5m3(4m4) – 5m3(-3m) - 5m3(1) = -20m7 + 15m4 - 5m3

(-3d + 10)(2d – 1) = (-3d)(2d) + (-3d)(-1) + (10)(2d) + (10)(-1) = -6d2 + 3d + 20d + (-10) = -6d2 + 23d - 10

(x2 – 4xy + y2)(5xy) = (x2)(5xy) + (-4xy)(5xy) + (y2)(5xy) = 5x3y – 20x2y2 + 5xy3

Write a polynomial for the area of the figure. A= L* W = (x + 5)(3x) = (3x)(x) + (3x)(5) = 3x2 + 15x

Pg 66 # 22 A box used for shipping a. Write a polynomial that represents the area of the base of the box. A= (n)(n+2) =(n)(n) + (n)(2) =n2 + 2n

b. Write a polynomial that represents the volume of the box. V= L * W * H =(n)(n+2)(n+4) =n[(n)(n) + (n)(4) + (2)(n) + (2)(4)] =n[n2 + 4n + 2n + 8] =(n)(n2) + (n)(6n) + (n)(8) =n3 + 6n2 + 8n c. What is the volume if the length of the shortest side is 8 inches? N=8 83 + 6(8)2 + 8(8) = 960 in3