**The formula**a^{3}- b^{3}= (a - b)(a^{2}+ ab + b^{2})

*Working forwards - Factorization*For example, the expression x

^{3}- 8y

^{3}can be expanded as follows:

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

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

= (x - 2y)(x.. which is the factored form of x^{2}+ 2xy + 4y^{2})

^{3}- 8y

^{3}

**Working backwards - Expansion**Since the opposite working of this formula is one step and requires almost no simplification, it is better to see an example of how this formula is applied in a problem like

x ^{2}+ 4x + 16x + 4

In the above example, if we multiply the fraction by

x - 4 |

x - 4 |

x ^{2}+ 4x + 16x + 4 ×

x ^{ }- 4x - 4

=

(x^{2} + 4x + 16) (x - 4) |

(x - 4) (x + 4) |

On comparing the numerator with the RHS of the above formula, it is a difference of two cubes, x

^{3}and 4

^{3}. So, factoring it, you get:

.. which is a simplified form of the original expression.

x ^{3}- 4^{3}(x + 4) (x - 4)