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Multiplication of Any Polynomial

Find the prod...

Question

Find the product of the following:
$(m - n) (m^{2} + m n + n^{2})$

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Solution

Product of $(m - n) (m^{2} + m n + n^{2})$
$= m (m^{2} + m n + n^{2}) - n (m^{2} + m n + n^{2})$
$= m^{3} + m^{2} n + m n^{2} - m^{2} n - m n^{2} - n^{3}$
$= m^{3} - n^{3}$
Hence, the answer is $m^{3} - n^{3} .$

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