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Expansion of (x^2 - y^2)

Factorise : ...

Question

Factorise : $(a^{2} - b^{2}) (a^{2} + a b + b^{2}) - a^{3} + b^{3}$

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Solution

We have,
$(a^{2} - b^{2}) (a^{2} + a b + b^{2}) - a^{3} + b^{3}$
$\Rightarrow (a^{2} - b^{2}) (a^{2} + a b + b^{2}) - (a^{3} - b^{3})$
$\Rightarrow (a - b) (a + b) (a^{2} + a b + b^{2}) - (a - b) (a^{2} + a b + b^{2})$
$\Rightarrow (a + b - 1) (a - b) (a^{2} + a b + b^{2})$

Hence, this is the answer.

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