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Basic Algebra
Multiplying Binomials: At a Glance

Introduction to Multiplying Binomials:

This is the last type of multiplication that we are going to learn in this unit. The good news is that there is nothing new to learn here. This is just applying the distributive property twice!

The most important part of multiplying two binomials is to make sure that you multiply each term in the first factor by each term in the second. This can get a bit confusing, so be careful!

(x-3)(2x +1)

Let's make things easier by changing subtraction symbol to adding a negative number.

(x + -3)(2x +1)

If we apply the distributive property twice, it would look like this:

distribution arrows (x + -3)(2x +1)

(x + -3)2x + (x + -3)1

x(2x) + -3(2x) + x(1) + -3(1)

2x^2 + -6x + x + -3

2x^2 + -5x + -3

Whew, that was exhausting. Let's learn two different methods to make this a little easier.

Method #1: Box Method

Create a two-by-two table. Place one factor on top, and the other on the side. It doesn't matter which goes where, since multiplication is commutative. Be sure to keep the subtraction and addition signs with the correct terms.

box method

Now, multiply each factor in the rows with each factor in the columns and write the products in the boxes.

box method 2

Add them all together,

2x^2 + x + -6x + -3

Combine like terms,

2x^2 + -5x + -3

And we're done!

Method #2: FOIL

FOIL stands for: First, Outer, Inner, Last. It is just a catchy way to remember each step.

First: multiply the first terms of each binomial.

X x 2X = 2X^2

Outer: multiply the outer terms of each binomial.

X x 1 = 1X

Inner: multiply the inner terms of each binomial.

(-3)2x = -6x

Last: multiply the last terms of each binomial.

(-3)1 = -3

Add them all together,

2x^2 + x + -6x + -3

Combine like terms,

2x^2 + -5x + -3

And it's the same as the Box Method!

If you look carefully you will see that the second method looks exactly like the examples from the distributive property section.

For each example we will multiply using both methods.

Multiplying Binomials Practice:

Example 1

(5y +3x)(8t - 1)


Example 2

(x-5)(x+5)


Example 3

(7x^2 + 3)(7x^2 + 3)


Exercise 1

Multiply: (2x - 8)(9x +4)


Exercise 2

Multiply (6a + b)(6a – b)


Exercise 3

A rectangular lawn 12 ft by 15 ft is going to be increased by a uniform amount (x) on each side. What will the new area be?


Exercise 4

Multiply -3y(x+6y)(3x - 4y)


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