Question
Factorise $p^4+ q^4+ p^2q^2$.
✓
Answer
We have,
$ p^4+q^4+p^2 q^2 $
$ =p^4+q^4+2 p^2 q^2-2 p^2 q^2+p^2 q^2 $
$ =p^4+q^4+2 p^2 q^2-p^2 q^2 $
$ =\left[\left(p^2\right)^2+\left(q^2\right)^2+2 p^2 q^2\right]-p^2 q^2 $
$ =\left(p^2+q^2\right)^2-(p q)^2 $
$ =\left(p^2+q^2+p q\right)\left(p^2+q^2-p q\right) $
$ p^4+q^4+p^2 q^2 $
$ =p^4+q^4+2 p^2 q^2-2 p^2 q^2+p^2 q^2 $
$ =p^4+q^4+2 p^2 q^2-p^2 q^2 $
$ =\left[\left(p^2\right)^2+\left(q^2\right)^2+2 p^2 q^2\right]-p^2 q^2 $
$ =\left(p^2+q^2\right)^2-(p q)^2 $
$ =\left(p^2+q^2+p q\right)\left(p^2+q^2-p q\right) $
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