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(a+b)(a-b) Expansion and Visualisation

Factorise: ...

Question

Factorise: $x^{4} - 3 x^{2} - 2 = 0$

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Solution

given, $x^{4} - 3 x^{2} + 2 = 0$

$x^{4} - 2 x^{2} - x^{2} + 2 = 0$

$\Rightarrow x^{2} (x^{2} - 2) - 1 (x^{2} - 2) = 0$

$\Rightarrow (x^{2} - 2) (x^{2} - 1) = 0$

$\Rightarrow (x^{2} - 2) (x - 1) (x + 1) = 0$

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