16x4 1=4x22 12=4x2+14x2 1 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160 ...

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Factorisation by Common Factors

Factorise:16 ...

Question

Factorise:
16x⁴ – 1

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Solution

$16 x^{4} - 1 = {(4 x^{2})}^{2} - 1^{2} = (4 x^{2} + 1) (4 x^{2} - 1) [a^{2} - b^{2} = (a + b) (a - b)] = (4 x^{2} + 1) [{(2 x)}^{2} - 1^{2}] = (4 x^{2} + 1) (2 x + 1) (2 x - 1) [a^{2} - b^{2} = (a + b) (a - b)]$

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