Difference of two squares

#### Tier: #Higher

Description

Recognising quadratic expressions in the form $ax^2-by^2$ where a and b are square numbers NB y will likely equal 1 to leave $ax^2-b$.

e.g. $x^2-36=(x+6)(x-6)$ $4x^2-25=(2x+5)(2x-5)$ $9x^{2}-16y^{2}=(3x+4y)(3x-4y)$

The difference of two squares (or DOTS as it is commonly referred) is a higher level concept which you are expected to recognise without any prompting. It crops up in several places, most notably Factorising quadratics, Algebraic fractions and Surds.

Links

Factorising quadratics