The simplest algebraic expression of $4 s t (s - t) - 6 s^{2} (t - t^{2}) - 3 t^{2} (2 s^{2} - s) + 2 s t (s - t)$ is _________.

- s t^{2}

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- 2 s t^{2}

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- 3 s t^{2}

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- 4 s t^{2}

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Solution

The correct option is B $- 3 s t^{2}$
Given expression
$4 s t (s - t) - 6 s^{2} (t - t^{2}) - 3 t^{2} (2 s^{2} - s) + 2 s t (s - t)$

On simplifying each term
$= 4 s^{2} t - 4 s t^{2} - 6 s^{2} t + 6 s^{2} t^{2} - 6 s^{2} t^{2} + 3 s t^{2} + 2 s^{2} t - 2 s t^{2}$

Clubbing similar algebraic terms
$= (4 - 6 + 2) s^{2} t + (- 4 - 2 + 3) s t^{2} + (6 - 6) s^{2} t^{2}$
$= (0) \times s^{2} t + (- 3) s t^{2} + (0) \times s^{2} t^{2}$
$= - 3 s t^{2}$

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Similar questions

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

(t + s^{2}) and (t^{2} - s) .

Find the product of $(t + s^{2})$ and $(t^{2} - s)$ .

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