Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$ x^4-y^4+x^2-y^2 $
$ x^4-y^4+x^2-y^2 $
✓
Answer
$ x^4-y^4+x^2-y^2 $
$ =\left(x^2\right)^2-\left(y^2\right)^2+\left(x^2-y^2\right) $
$ =\left(x^2+y^2\right)\left(x^2-y^2\right)+\left(x^2-y^2\right) $
$ =\left(x^2-y^2\right)\left(x^2+y^2+1\right) $
$ =(x+y)(x-y)\left(x^2+y^2+1\right) $
$ =\left(x^2\right)^2-\left(y^2\right)^2+\left(x^2-y^2\right) $
$ =\left(x^2+y^2\right)\left(x^2-y^2\right)+\left(x^2-y^2\right) $
$ =\left(x^2-y^2\right)\left(x^2+y^2+1\right) $
$ =(x+y)(x-y)\left(x^2+y^2+1\right) $
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