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