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Multiplying Binomials

In this video, we are going to look at how to multiply binomials. Some teachers teach this as FOIL (First, Outer, Inner Last).
For example:
To multiply (x+5)(x-3) we have to distribute twice.
When we distribute the x to the terms in the second binomial, we get x^2 and -3x. When we distribute the 5 to both terms, we get 5x and -15. So now we are left with
x^2-3x+5x-15
From here, we want to combine like terms, to give us a final answer of
x^2+2x-15

Video-Lesson Transcript

In this lesson, we’re going to discuss how to multiply binomials.

For example:

We have x + 5 multiplied by x - 3.

Here we have two two-term equation.

To multiply them, we have to distribute twice.

So, let’s multiply the first term of the first equation to the first term of the second equation then multiply the first term of the first equation to the second term of the second equation.

Then, do the same with the second term of the first equation.

(x + 5)(x - 3)

Let’s have x \times x = x^{2} and x \times {-3} = {-3x}.

Then, 5 \times x = 5x and 5 \times {-3} = {-15}.

So we have

x^{2} - 3x + 5x - 15

Let’s combine like terms and our final answer is

x^{2} + 2x - 15

Multiplying Binomials

Let’s have another example

(2x - 4)(3x + 8)

First, let’s distribute the first term of the first equation to each term of the second equation.

2x \times 3x = 6x^{2}
2x \times 8 = 16x

Next, let’s distribute the second term of the first equation to each term of the second equation.

{-4} \times 3x = {-12x}
{-4} \times 8 = {-32}

So now we have

6x^{2} + 16x - 12x - 32

Let’s combine the like terms.

Our answer is

6x^{2} + 4x - 32

To multiply binomials, you just have to distribute each term twice.