### The Formula

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

#### Working forwards - Expansion

For example, the expression (4x - y)^{2}can be expanded as follows:

= (4x)^{2}+ (y)^{2}- 2(4x)(y)

= 16x^{2}+ y^{2}- 8xy

#### Working backwards - Factorization

For example, the expression x^{2}+ 81y

^{2}- 18xy can be factored as follows:

xOn comparing it with a^{2}+ (9y)^{2}- 2(x)(9y)

^{2}+ b

^{2}- 2ab

(x - 9y).. which is the factored form.^{2}