*:*

**The formula**(a - b)^{3}= a^{3}- b^{3}- 3ab(a - b)

**Working forwards: Expansion**For example, (x - 2y)

^{3}can be expanded as follows:

= x^{3}- (2y)^{3}- 3*x*2y(x - 2y)

= x^{3}- 8y^{3}- 6xy(x - 2y)

= x^{3}- 8y^{3}- 6x^{2}y + 12xy^{2}

**Working backwards: Factorization**For example, the expression 27x

^{3}- 64y

^{3}- 36x

^{2}y + 36xy

^{2}can be factored as follows:

= (3x)on comparing with a^{3}- (4y)^{3}- 3*(3x)^{2}*4y + 3*3x*(4y)^{2}

^{3}- b

^{3}- 3ab(a - b),

= (3x - 4y)^{3}