Question
Verify the following:
$ (p-q)\left(p^2+p q+q^2\right)=p^3-q^3 $
$ (p-q)\left(p^2+p q+q^2\right)=p^3-q^3 $
✓
Answer
$ (p-q)\left(p^2+p q+q^2\right)=p^3-q^3 $
$ =p\left(p^2+p q+q^2\right)-q\left(p^2+p q+q^2\right) $
$ =p^3+p^2 q+p q^2-q p^2-p q^2-q^3 $
$ =p 3-q 3 $
= RHS
Hence verified
$ =p\left(p^2+p q+q^2\right)-q\left(p^2+p q+q^2\right) $
$ =p^3+p^2 q+p q^2-q p^2-p q^2-q^3 $
$ =p 3-q 3 $
= RHS
Hence verified
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