Question

Factorise
x4-y4+x2-y2

Answer 1

Answer:

$x^{4}-y^{4}+x^{2}-y^{2}\\</p><p>=(x+y)(x-y)[(x^{2}+y^{2}+1]$

Step-by-step explanation:

$x^{4}-y^{4}+x^{2}-y^{2}\\=[(x^{2})^{2}-(y^{2})^{2})]+x^{2}-y^{2}\\=(x^{2}+y^{2})(x^{2}-y^{2})+x^{2}-y^{2}$

\* By algebraic identity :

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

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

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

Therefore,

$x^{4}-y^{4}+x^{2}-y^{2}\\</p><p>=(x+y)(x-y)[(x^{2}+y^{2}+1]$

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Answer 2

(x-y)2 (x+y)2 (x-y)2