1. Objective
SWBAT use special product patterns to multiply polynomials

2. First Outer Inner Last “Multiply Using FOIL”
When multiplying a binomial and another polynomial use the method.
FOIL
First
Outer
Inner
Last

3. “Multiply Using FOIL”
(x – 4)
(3x + 2)
combine like terms

4. Section 9.3 “Find Special Products of Polynomials”
When squaring binomials, you can use the following patterns to help you.
Binomial Square Pattern (addition)
(a + b)²
a² + 2ab + b²
(a + b)(a + b)
(x + 5)²
x² + 10x + 25
(x + 5)(x + 5)

5. Section 9.3 “Find Special Products of Polynomials”
When squaring binomials, you can use the following patterns below to help you.
Binomial Square Pattern (subtraction)
(a – b)²
a² – 2ab + b²
(a – b)(a – b)
(2x – 4)²
4x² – 16x + 16
(2x – 4)(2x – 4)

6. “Using the Binomial Square Patterns and FOIL”
combine like terms

7. “Using the Binomial Square Patterns and FOIL”
(5x – 2y)²
(5x – 2y)
(5x – 2y)
square pattern
combine like terms

8. Sum and Difference Pattern
(a + b)
(a – b)
a² – b²
(a + b)
(a – b)
“The difference
of two squares”
combine like terms

9. Sum and Difference Pattern
(x + 3)
(x – 3)
x² – 9
combine like terms
“The difference
of two squares”

10. Word Problem (2x +20)(2x + 22) 4x² + 40x + 44x + 440 4x² + 84x + 440
You are designing a frame to surround a rectangular picture. The width of the frame around the picture is the same on every side. The dimensions of the picture are shown below 22in. by 20in. Write a polynomial that represents the total area of the picture and the frame. x
(2x +20)(2x + 22)
22 in.
FOIL
20in x x
4x² + 40x + 44x + 440
4x² + 84x + 440 x