The formula:
Working forwards: Expansion
For example, (x - 2y)3 can be expanded as follows:
For example, the expression 27x3 - 64y3 - 36x2y + 36xy2 can be factored as follows:
(a - b)3 = a3 - b3 - 3ab(a - b)
Working forwards: Expansion
For example, (x - 2y)3 can be expanded as follows:
= x3 - (2y)3 - 3*x*2y(x - 2y)
= x3 - 8y3 - 6xy(x - 2y)
= x3 - 8y3 - 6x2y + 12xy2Working backwards: Factorization
For example, the expression 27x3 - 64y3 - 36x2y + 36xy2 can be factored as follows:
= (3x)3 - (4y)3 - 3*(3x)2*4y + 3*3x*(4y)2on comparing with a3 - b3 - 3ab(a - b),
= (3x - 4y)3
