Question

factorise (x^4-1) using alebragic identifie
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Answer 1

$Given \: x^{4} - 1$

$= (x^{2})^{2} - 1^{2}$

$= (x^{2} + 1 )(x^{2} - 1 )$

/* By algebraic identity */

$\boxed{\pink{ a^{2} - b^{2} = (a+b)(a-b)}}$

$= (x^{2} + 1 )(x^{2} - 1^{2} )$

$= (x^{2} + 1 )(x + 1 )(x-1)$

Therefore.,

$\red{Factors \: of \: x^{4} - 1}$

$\green {= (x^{2} + 1 )(x + 1 )(x-1) }$

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