Simplify:
$(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$ .

m^{4} - n^{4} m^{2}

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m^{4} + n^{4} m^{2}

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m^{4} + n^{4}

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m^{4} + n^{4} m^{2} + 2 m^{3} n^{2}

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Solution

The correct option is B $m^{4} + n^{4} m^{2}$
Given, $(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$ .

We know, $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ .

Then,
$(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$
$= (m^{2})^{2} - 2 (m^{2}) (n^{2} m) + (n^{2} m)^{2} + 2 m^{3} n^{2}$
$= m^{4} - 2 m^{3} n^{2} + n^{4} m^{2} + 2 m^{3} n^{2}$
$= m^{4} + n^{4} m^{2}$ .

Therefore, option $B$ is correct.

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