Difference of Two Squares

This is a quadratic expression where:

• there are only 2 terms.

• both are 'squares'.

• there is a minus sign between the terms.

Worked examples

1) Factorise x² - 4  ~   Answer = (x + 2)(x - 2)

Method

• Draw 2 brackets.

• Write the square root of the first term in each bracket.

• Write the square root of the second term in each bracket.

• Write a '+' in one bracket and a '-' in the other.

2) Factorise 16x² - 81  ~  Answer = (4x + 9)(4x - 9)

3) Factorise 16x² - 64  ~  Gives: 16(x² - 4)  ~  Answer = 16(x + 2)(x - 2)

• The factorising process can be simplified if all terms are divisible by the same amount. In this case, both of the original terms were divisible by 16.