If $x - y = 4$ and $x y = 21$ , then $x^{3} - y^{3} = . . . . . . . . . .$

361

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316

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- 188

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None of these

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Solution

The correct option is B $316$
$x - y = 4$
Cubing on both sides, we get
$(x - y)^{3} = (4)^{3}$
$x^{3} - y^{3} - 3 x y (x - y) = 64$ .......... $(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$x^{3} - y^{3} - 3 (21) (4) = 64$
$x^{3} - y^{3} = 316$

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