Multiplying Terms Using the FOIL Method

Hello, and welcome to this video about multiplying terms using the FOIL method. Today we’ll learn a strategy for multiplying two-digit numbers. We’ll also learn how to apply this strategy to multiplying polynomials with two terms.

Before we get started, let’s review a few things. First, a polynomial is an expression that can have many terms with variables, coefficients, and positive exponents. These terms can be added, subtracted, multiplied, and divided.

Today we’re going to talk about polynomials with two terms. Polynomials with two terms are called binomials.

Examples of binomials are \(2x+7, 30\text{ }+8,\text{ and}\text{ }5x^{2}-3\). All binomials have two terms that are separated by an operation sign.

The FOIL method is a technique that’s used to remember the steps for multiplying two binomials. The letters in the word FOIL stand for First, Outer, Inner, and Last. The product of two binomials is the sum of multiplying the first terms, outer terms, inner terms, and last terms:

Let’s look at an example of multiplying two-digit numbers using the FOIL method.

So consider the multiplication problem \(35\times 56\). To solve using the FOIL method, start by writing each term as a binomial. In other words, split each number into two numbers according to their place value. So \(35\) is \((30+5)\) and \(56\) is \((50+6)\).

Now that each number is written as a binomial, we can apply the FOIL method.

So the F in FOIL stands for First. We’re going to multiply our first terms by one another.

Then, the O in FOIL stands for Outer, so we’re going to multiply our outer numbers.

Then the I in FOIL stands for Inner, so we’re going to multiply the inner terms.

And finally, we have the L in FOIL, which stands for Last. So the last two terms of our binomials are 5 and 6.

Now, all we have to do is add this together and we’ll get a total of: \(1,500+180+250+30=1,960\).

Let’s look at another multiplication problem where we can apply the FOIL method.

Makayla has 24 filled photo albums. If each album holds 48 photos, how many photos does she have in all?

To solve this problem, we need to multiply \(24\times 48\). To solve using the FOIL method, start by writing each term as a binomial, so \(24\) is \((20+4)\) times 48 is \((40+8)\).

Now that each number is written as a binomial, we can apply the FOIL method.

The F in FOIL stands for First, so we’ll multiply our first terms by one another.

Then we’ll do our outer terms because that’s what the O stands for.

Next comes I, which stands for Inner.

And finally, we’re going to do the L, which is the last two terms.

Now, all we have to do is add these four numbers together and we get: \(800+160+160+32=1,152\). So Makayla has 1,152 photos altogether.

The FOIL method is a good strategy for multiplying two-digit numbers, especially if you don’t have a calculator on hand. The FOIL method can also be applied to binomials with variables and exponents. Let’s look at another problem together:

Notice that this problem has the variable \(x\) in the terms \(6x\) and \(4x\). Even so, we can apply the FOIL method to multiply.

So we’re going to start by multiplying our first terms together.

Then we’re going to multiply our outer terms.

Next, we’ll do our inner terms, which is \(3\) and \(4x\).

And finally, we’ll do our last terms.

Now all we have to do is add our like terms right here.

So that’s our answer: \(24x^{2}+54x+21\).

I have one more problem for you to analyze on your own. This one is a little bit more challenging, but I know you can do it.

The length of a rectangle is \((5x+1)\). Its width is \((2x+8)\). Write a polynomial for the area of the rectangle in standard form, \(ax^{2}+bx+c\).

Pause the video, analyze the word problem, and see if you can solve it by yourself. When you’re ready, resume the video, and we’ll go over the answer together.

Now that you’ve tried this problem, let’s go over it together.

To find the area of a rectangle, multiply its length by its width.

Since the length is \((5x+1)\), we can write that. And the width is \((2x+8)\).

Now we can multiply using the FOIL method.

So the first two terms are \(5x\) and \(2x\).

Plus our outer terms.

Plus our inner terms.

And finally, our last terms.

We add all these together.

Now all we have to do is combine our like terms.

Therefore, the area of the rectangle is \(10x^{2}+42x+8\).

Great job!

I hope this video about multiplying terms using the FOIL method was helpful. Thanks for watching, and happy studying!

FOIL Method Practice Questions