Identity

Difference of two squares

Algebra • Expressions • Algebraic Identities

Formula

a^{2} - b^{2} = (a + b) (a - b)

For all real

a

and

b

a^{2} - b^{2} = (a + b) (a - b)

How to use it

1Read it left to right to factorise, right to left to simplify a product.
2Works when $a$ or $b$ is itself an expression, e.g. $(x + 1)^{2} - 4 = (x + 3) (x - 1)$ .
3Chain it: $a^{4} - b^{4} = (a^{2} + b^{2}) (a^{2} - b^{2}) = (a^{2} + b^{2}) (a + b) (a - b)$ .

Evaluate

10 1^{2} - 9 9^{2}

without long multiplication.

Step-by-step

1
$10 1^{2} - 9 9^{2} = (101 + 99) (101 - 99)$
Why: Recognise the difference-of-squares form.
2
$= 200 \times 2 = 400$

Answer

400

Watch out

There is no analogous real factorisation of

a^{2} + b^{2}

Also known as

a squared minus b squared, factorise difference of squares