The product of (t+s2) and (t2−s) is

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Question

The product of $(t + s^{2})$ and $(t^{2} - s)$ is

Options:

A .

t^{3} + s^{2} t^{2} - s t - s^{3}

B .

t^{3} + s^{2} t^{2} - s t - s^{2}

C .

t^{3} + s^{2} t^{2} - 2 s t - s^{3}

D .

t^{3} + t^{2} - s t - s^{3}

Answer: Option A
:
A

$(t + s^{2}) (t^{2} - s) = [t (t^{2} - s) + s^{2} (t^{2} - s)]$
$= t^{3} - t s + s^{2} t^{2} - s^{3}$

$= t^{3} + s^{2} t^{2} - s t - s^{3}$

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