Year 9: Factorise difference of squares

This cheat sheet will help you factorise expressions that are a difference of squares. A difference of squares follows the pattern: $a^2-b^2$

Formula

The formula to factorise a difference of squares is:

    $a^2-b^2=(a+b)(a-b)$
  

Examples

Example 1:

Factorise: $x^2-9$

    $x^2-9=x^2-3^2$
    = $(x+3)(x-3)$
  

Example 2:

Factorise: $4y^2-25$

    $4y^2-25={\left(2y\right)}^2-5^2$
    = $(2y+5)(2y-5)$
  

Key points:

• Remember to identify the perfect squares.
• The terms being squared are 'a' and 'b'.
• Always check your answer by expanding $(a+b)(a-b)$ to see if you get the original expression.