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 $x^{2} + 2x - 15$ 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. $6x^{2} + 4x - 32$