$(m - n)^{6} - 8 m^{3} =$

{(m - n)^{3} + 4 m} {(m - n)^{3} - 2 m^{2}}

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{(m - n)^{3} - (2 m)^{3}} {(m - n)^{3} + (m^{3})}

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{(m - n)^{2} - 2 m} {(m - n)^{4} + (m - n)^{2} 2 m + 4 m^{2}}

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Solution

The correct option is C ${(m - n)^{2} - 2 m} {(m - n)^{4} + (m - n)^{2} 2 m + 4 m^{2}}$
We need ti find value of $(m - n)^{6} - 8 m^{3}$
We know the identity, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
Here $a = (m - n)^{2}, b = 2 m$
Therefore, $((m - n)^{2})^{3} - (2 m)^{3} = {(m - n)^{2} - 2 m} {(m - n)^{4} + (m - n)^{2} 2 m + 4 m^{2}}$

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