Difference of Squares
(KS4, Year 10)

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. difference_of_squares_numbers 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: difference_of_squares 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:

difference of squares factored

Lesson Slides

The slider below shows why a difference of squares can be factored as a2 − b2 = (a + b)(a − b).
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This page was written by Stephen Clarke.