Simplify the following:
$(m + n) (m^{2} - m n + n^{2})$

m^{3} + n^{3}

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m^{3} - n^{3}

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m^{3} + 2 n^{3}

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None of these

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Solution

The correct option is A $m^{3} + n^{3}$
We simplify the given expressions $(m + n) (m^{2} - m n + n^{2})$ as shown below:

$(m + n) (m^{2} - m n + n^{2}) = m (m^{2} - m n + n^{2}) + n (m^{2} - m n + n^{2}) = m^{3} - m^{2} n + m n^{2} + n m^{2} - m n^{2} + n^{3} = m^{3} + n^{3} + (- m^{2} n + m^{2} n) + (m n^{2} - m n^{2}) (C o m b i n i n g l i k e t e r m s) = m^{3} + n^{3}$

Hence, $(m + n) (m^{2} - m n + n^{2}) = m^{3} + n^{3}$ .

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