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Factorisation using algebraic identities

Question 92 x...

Question

Question 92 (xxi)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$p^{5} - 16 p$

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Solution

$p^{5} - 16 p = p (p^{4} - 16) = p [(p^{2})^{2} - 4^{2}] = p (p^{2} + 4) (p^{2} - 4) = p (p^{2} + 4) (p^{2} - 2^{2}) = p (p^{2} + 4) (p + 2) (p - 2)$

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Factorisation using algebraic identities

Standard VIII Mathematics

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