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**The formula**:

`(a + b)^3 = a^3 + b^3 + 3ab(a + b)`

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**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}

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**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}