1. Multiplying Binomials
Section 8-3 Part 1 & 2

2. Goals
Goal
Rubric
To multiply two binomials or a binomial by a trinomial.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary
None

4. Multiplying Polynomials
3 Methods for multiplying polynomials
Using the Distributive Property
Can be used to multiply any two polynomials
Using a Table or The Box Method
Using FOIL
Can only be used to multiply two binomials

5. Method 1: Distributive Property
To multiply a binomial by a binomial, you can apply the Distributive Property more than once:
(x + 3)(x + 2) =

6. Example: Multiply Using Distributive Property
(s + 4)(s – 2)

7. Your Turn:
Multiply.
(a + 3)(a – 4)

8. Your Turn:
Multiply.
(y + 8)(y – 4)

9. Method 2: Box Method
Visual model for distributing in polynomial products, works with any polynomial.
Box method
2 x 2 parts =
2 rows 2 columns

10. Example: Multiply Using Box Method
(x – 3)(4x – 5)

11. Your Turn:
Multiply
(3x + 1)(x + 4)

12. Your Turn:
Multiply
(2x - 5)(4x + 3)

13. Method 3: FOIL F O I L (x + y)(x + z) = x + xz xy yz
The product can be simplified using the FOIL method: multiply the First terms, the Outer terms, the Inner terms, and the Last terms of the binomials. F O I L
First
Last
(x + y)(x + z) = x 2 + xz xy yz
Inner
Outer

14. Example: Multiply Using FOIL
(x + 3)(x + 2)
“First Outer Inner Last”, shortcut for distributing, only works with binomial-binomial products. F
1. Multiply the First terms. (x + 3)(x + 2) x x = x2  O
2. Multiply the Outer terms. (x + 3)(x + 2) x 2 = 2x  I
3. Multiply the Inner terms. (x + 3)(x + 2) x = 3x  L
4. Multiply the Last terms. (x + 3)(x + 2) = 6 
(x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6 F O I L

15. Example: FOIL

16. Your Turn:
Multiply.
A. (m – 2)(m – 8)
B. (x + 3)(x + 4)

17. Your Turn:
Multiply.
(x – 3)(x – 1)

18. Your Turn:
Multiply.
(2a – b2)(a + 4b2)

19. To multiply polynomials with more than two terms, you can use the Distributive Property several times.
Multiply (5x + 3) by (2x2 + 10x – 6):

20. Write the product of the monomials in each row and column:
You can also use the Box Method to multiply polynomials with more than two terms Multiply (5x + 3) by (2x2 + 10x – 6):
2x2
+10x –6 5x +3
Write the product of the monomials in each row and column:
To find the product, add all of the terms inside the box by combining like terms and simplifying if necessary.

21. Example:
Multiply.
(x – 5)(x2 + 4x – 6)

22. Your Turn: Multiply. (3x + 1)(x3 + 4x2 – 7) x3 4x2 –7 3x +1
Write the product of the monomials in each row and column. x3
4x2 –7 3x +1
Add all terms inside the rectangle.

23. Your Turn:
Multiply.
(x + 3)(x2 – 4x + 6)

24. Your Turn:

25. Example: Application
The width of a rectangular prism is 3 feet less than the height, and the length of the prism is 4 feet more than the height.
Write a polynomial that represents the area of the base of the prism.
A = l  w
A = l w 

26. Your Turn: Find the area of the base when the height is 5 ft.
The width of a rectangular prism is 3 feet less than the height, and the length of the prism is 4 feet more than the height.
Find the area of the base when the height is 5 ft.
A = h2 + h – 12