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: a² - b²

Formula

The formula to factorise a difference of squares is:

    a2 - b2 = (a + b)(a - b)
  

Examples

Example 1:

Factorise: x² - 9

    x2 - 9 = x2 - 32
    = (x + 3)(x - 3)
  

Example 2:

Factorise: 4y² - 25

    4y2 - 25 = (2y)2 - 52
    = (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.