In this explainer, we will learn how to multiply the sum of two terms by their difference to get the polynomial known as the difference of two squares.

The product of two binomials is a difference of two squares if it is in the form

If we expand these two brackets we get which simplifies to

This is a useful result that allows us to quickly expand expressions that are presented in this form. Let us look at a couple of examples.

### Example 1: Finding the Sum and Difference of Two Squares

Expand the product .

### Answer

As this expression is in the form , we know that the expanded form is

Here, and , so the expansion is which simplifies to

Now, let us look at a couple of similar examples with more complicated terms.

### Example 2: Finding the Sum and Difference of Two Squares

Use the difference of two squares identity to expand .

### Answer

As this expression is in the form , we know that the expanded form is

Here, and , so the expansion is which simplifies to

### Example 3: Finding the Sum and Difference of Two Squares

Expand the product .

### Answer

As this expression is in the form , we know that the expanded form is

Here, and , so the expansion is which simplifies to

Now, let us have a look at some problems where we need to apply the method that we have just been looking at.

### Example 4: Using the Sum and Difference of Two Squares to Solve Problems

If and , what is the value of ?

### Answer

Recall that

We are told that and . Therefore, we can calculate by finding the product .

### Example 5: Using the Sum and Difference of Two Squares to Solve Problems

Given that and , find .

### Answer

Recall that

Here, we know the value of and the value of . Substituting these values into the difference of two squares result, we get

Dividing both sides by 5, we find that