Difference of Two Squares

## Difference of Two Squares

Expanding the expression (a + 3)(a - 3) gives an answer of a^2 - 9: there is no a term.

a^2 - 9 can be written as a^2 - 3^2: both terms are squared and the subtraction gives the difference.

Note that the constant in the expanded expression is a negative.

This is known as the difference of two squares.

## Example 1

Factorise b^2 - 81

No b term and √81 = 9 and -9, so is the difference of two squares.

Answer: (b + 9)(b - 9)

## Example 2

Show a^2x^2 - y^2 as the difference of two squares.

First term: sqrt(a^2x^2) = ax

Second term: sqrt(y^2) = +y text( and ) -y

a^2x^2 - y^2 = (ax + y)(ax - y)

Answer: (ax + y)(ax - y)