As we know that #160; (x+y)(x y)=x^2 y^2 a^4 b^4=(a^2)^2 (b^2)^2=(a^2+b^2)(a^2 b^2)=(a^2+b^2)((a)^2 (b)^2)=(a^2+b^2)(a b)(a+b) ...

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Expansion of (x^2 - y^2)

Factorise a...

Question

Factorise $a^{4} - b^{4}$

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Solution

As we know that
$(x + y) (x - y) = x^{2} - y^{2}$
$a^{4} - b^{4} = (a^{2})^{2} - (b^{2})^{2} = (a^{2} + b^{2}) (a^{2} - b^{2}) = (a^{2} + b^{2}) ((a)^{2} - (b)^{2}) = (a^{2} + b^{2}) (a - b) (a + b)$

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