**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 sum 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)