Download 8-2 Multiplying Polynomials using the Distributive

8-2 Multiplying Polynomials
GOAL:
MULTIPLY TWO POLYNOMIALS TOGETHER
USING THE DISTRIBUTIVE PROPERTY
ELIGIBLE CONTENT:
A1.1.1.5.1
Vocabulary
 Distributive Property – multiplying the term
outside the parentheses by every term inside the
parentheses.
 When you multiply variables together:
You ADD the exponents!
Monomial times Polynomial
3x (4 x  6 x  10)
2
2
12x  18x 3  30x 2
4
Examples
1. 4 x(3x  8 x  2)
 12 x  32 x  8 x
2.  2 x (4 x  9 x  7)
  8 x  18 x  14 x
2
2
2
3
4
2
3
2
Find 3x(2x2 + 3x + 5).
A. 6x2 + 9x + 15
B. 6x3 + 9x2 + 15x
C. 5x3 + 6x2 + 8x
D. 6x2 + 3x + 5
Binomial times Polynomial
 Distribute each term of the binomial.
(2 x  4)( 4 x  3x  8)
2
2 x  4 x 2  2x  3x  2 x  8  4  4 x 2 4  3x  4 8
8x 3  6x 2  16x  16x 2  12 x  32
8x  10x  4x  32
3
2
Vocabulary
 Box Method – a method used to multiply
polynomials.
The Box Method
(2 x  8)(3x  2 x  7)
2
3x
 2x
2
 4x
3
2x
6x
8
 24x
2
 16x
2
6x  28x  2x  56
3
2
7
 14 x
 56
Examples

1. 3x  2 4 x  9 x  7
2
2



2
x

5
4
x
 3x  1
2.

 12 x  19 x  3x  14
3
2
 8 x  26 x  13x  5
3
2
Find (3z + 2)(4z2 + 3z + 5).
A. 12z3 + 9z2 + 15z
B. 8z2 + 6z + 10
C. 12z3 + z2 + 9z + 10
D. 12z3 + 17z2 + 21z + 10
Practice
 Worksheet – “8-2 Multiplying Polynomials”
Simplifying Expressions
1.
2p(-4p2 + 5p) – 5(2p2 + 20)
-8p3 – 100
2.
3(5x2 + 2x – 4) – x(7x2 + 2x – 3)
-7x3 + 13x2 + 9x – 12
Simplify 5(4y2 + 5y – 2) + 2y(4y + 3).
A. 4y2 + 9y + 1
B. 8y2 + 5y – 6
C. 20y2 + 9y + 6
D. 28y2 + 31y – 10
Homework
 Page 475 #18-28 even
 Page 483 #8, 9, 25, 26