We write it as ( x ^ 2 ) #160;^ 2 1 ^ 2 . Hence x ^ 4 1=( x ^ 2 ) #160;^ 2 1 ^ 2 =( x ^ 2 1)( x ^ 2 +1) Here ( x ^ 2 ) #160;^ ...

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Factorisation Using Algebraic Identities

Factorise x...

Question

Factorise $x^{4} - 1$ .

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Solution

We write it as ${(x^{2})}^{2} - 1^{2}$ . Hence
$x^{4} - 1 = {(x^{2})}^{2} - 1^{2} = (x^{2} - 1) (x^{2} + 1)$
Here ${(x^{2})} - 1 = (x - 1) (x + 1)$ . Thus
$x^{4} - 1 = {(x^{2})}^{2} - 1^{2} = (x^{2} - 1) (x^{2} + 1) = (x - 1) (x + 1) (x^{2} + 1)$

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