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Factors of Algebraic Expressions and Factorisation

Factorise : ...

Question

Factorise :
$x^{4} + 4$

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Solution

$x^{4} + 4$
$= (x^{4} + 4 x^{2} + 4) - 4 x^{2}$
$= (x^{2} + 2^{2}) - (2 x)^{2}$
$= (x^{2} + 2 - 2 x) (x^{2} + 2 + 2 x)$
$= (x^{2} - 2 x + 2) (x^{2} + 2 x + 2)$

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