2.2-Multiply Polynomialsa3 + a3 = 2a3

b4(b3) = b4+3 = b7

Area = length * widthVolume = length * width * height

MEMORIZE!!

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

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

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

A= L* W

= (x + 5)(3x)

= (3x)(x) + (3x)(5)

= 3x2 + 15x

Write a polynomial for the area of the figure.

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=883 + 6(8)2 + 8(8)= 960 in3