The expression ${(5 x - 8)}^{3} - {(3 x - 8)}^{3} - 6 x (5 x - 8) (3 x - 8)$ , when simplified gives:

8 x^{3}

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5 x

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3 x^{2}

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Solution

The correct option is A $8 x^{3}$
Given expression is $(5 x - 8)^{3} - (3 x - 8)^{3} - 6 x (5 x - 8) (3 x - 8)$ .

Let $5 x - 8 = a, 3 x - 8 = b$ , then the given expression is:
$a^{3} - b^{3} - 3 (a - b) \times a b = {(a - b)}^{3}$
$\Rightarrow [(5 x - 8) - (3 x - 8)]^{3} = [5 x - 3 x - 8 + 8]^{3}$
$\Rightarrow (2 x)^{3} = 8 x^{3}$ .

Therefore, option $A$ is correct.

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