Question 88 (xiii)

Factorise the following expression.

$(a^{3} x - x^{4} + a^{2} x^{2} - a x^{3})$

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Solution

We have, $(a^{3} x - x^{4} + a^{2} x^{2} - a x^{3})$
$= x (a^{3} - x^{3} + a^{2} x - a x^{2}) = x (a^{3} + a^{2} x - x^{3} - a x^{2})$
$= x [a^{2} (a + x) - x^{2} (x + a)]$
$= x [(x + a) (a^{2} - x^{2})] = x (a^{2} - x^{2}) (a + x)$

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