Question

factorise the following expresions : x4 - y4 + x2 - y2​

Answer 1

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

Answer:

x4-y4+x2-y2

=[(x2)2 - (y2)2] +x2-y2

=(X2+y2)(x2-y2)+x2-y2