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Cube of a sum: `(a + b)^3`

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:
= x3 + (2y)3 + 3*x*2y(x + 2y)
= x3 + 8y3 + 6xy(x + 2y)
= x3 + 8y3 + 6x2y + 12xy2

Working 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)2
on comparing with a3 + b3 + 3ab(a + b),
= (3x + 4y)3