What Is a Difference of Squares?

What Is a Difference of Squares?

A difference of squares is square number (a number multiplied by itself) subtracted from another square number.

A Real Example of a Difference of Squares

It is easier to understand a difference of squares with an example.

In this example,

  • 32 = 3 × 3 = 9 (3 squared).

  • 22 = 2 × 2 = 4 (2 squared).

The two numbers are square numbers. They are squares.

Two numbers are being subtracted from each other. It is a difference of squares.

A Difference of Squares in General

In general, we can use symbols instead of numbers:

a and b are both integers (whole numbers).

How to Factor a Difference of Squares

A difference of squares can be factored into two brackets:

Why the Factoring Works

The slider below shows why a difference of squares can be factored as a2 − b2 = (a + b)(a − b).

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See Also

What is a square number? What is an integer?