This document reviews three methods for multiplying polynomials: the distributive property, FOIL method, and box method. It provides examples of multiplying binomials like (2x + 3)(5x + 8) and (y + 4)(y - 3) using each method. The key steps of each method are defined, including the FOIL acronym for the order of multiplying terms in binomials.

1. Objective
Review Multiplying Polynomials
By the end of this presentation, you
should review the FOIL method, Box
method and the distributive property.
Designed by Skip Tyler, Varina High School

2. Remember, there are 3 techniques you
can use for multiplying polynomials.
can use for multiplying polynomials.
It’s all about how you write it…
» Distributive Property
» FOIL
3)Box Method

3. Multiply. (2x + 3)(5x + 8)
Using the distributive property,multiply
2x(5x + 8) + 3(5x + 8).
2
10x + 16x + 15x + 24
Combine like terms.
2
10x + 31x + 24
A shortcut of the distributive property is
called the FOIL method.

4. The acronym FOIL reminds
you to multiply the:
you to multiply the:
First terms
Outer terms
Inner terms
Last terms
of the 2 binomials

5. The FOIL method is ONLY used when
you multiply 2 binomials. It is an acronym
and tells you which terms to multiply.
Use the FOIL method to multiply the
following binomials:
(y + 3)(y + 7).

6. The third method is the Box Method. This
method works for every problem!
Here’s how you do it.
Multiply (3x – 5)(5x + 2) 3x -5
Draw a box. Write a
polynomial on the top and
side of a box. It does not
5x
matter which goes where.
This will be modeled in the +2
next problem along with
FOIL.

7. Multiply (3x - 5)(5x + 2)
2
First terms: 15x 3x -5
Outer terms: +6x
Inner terms: -25x 5x 15x2 -25x
Last terms: -10
Combine like terms.
2
+2 +6x -10
15x - 19x – 10
You have 3 techniques. Pick the one you like the best!

8. Multiply (2x - 5)(x2 - 5x + 4)
Combine like terms!
2
x -5x +4
2x
Now you do the rest.... then click to reveal the answer
-5
3 2
2x – 15x + 33x - 20

9. Multiply (y + 4)(y – 3)
Which of the answers listed is the correct one.
Click on the screen to find out!
• y2 + y – 12
• y2 – y – 12
• y2 + 7y – 12
4. y2 – 7y – 12
• y2 + y + 12
• y2 – y + 12
• y2 + 7y + 12
8. y2 – 7y + 12

10. Multiply (2a – 3b)(2a + 4b)
Try another one on your own. You choose the method.
Click to reveal the answer.
1. 4a2 + 14ab – 12b2
2. 4a2 – 14ab – 12b2
• 4a2 + 8ab – 6ba – 12b2
• 4a2 + 2ab – 12b2
• 4a2 – 2ab – 12b2