1. 2.2-Multiply Polynomials a3 + a3 = 2a3 b4(b3) = b4+3 = b7
Area = length * width
Volume = length * width * height
MEMORIZE!!

2. =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

3. 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

4. (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

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

6. 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

7. -5m3(4m4 – 3m + 1) = -5m3(4m4) – 5m3(-3m) - 5m3(1)
Examples
-5m3(4m4 – 3m + 1)
= -5m3(4m4) – 5m3(-3m) - 5m3(1)
= -20m7 + 15m4 - 5m3

8. (-3d + 10)(2d – 1)
= (-3d)(2d) + (-3d)(-1) + (10)(2d) + (10)(-1)
= -6d2 + 3d + 20d + (-10)
= -6d2 + 23d - 10

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

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

11. 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

12. 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