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Algebraic Identity (a-b)^3

The value of ...

Question

The value of $(x + 3)^{3} - (x - 3)^{3}$ is :

0

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1 - x^{3}

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3 x^{2} - 5

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18 x^{2} + 54

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Solution

The correct option is D $18 x^{2} + 54$
We have, $(a + b)^{3} - (a - b)^{3} = 2 (b^{3} + 3 a^{2} b)$
$(x + 3)^{3} - (x - 3)^{3} = 2 [3^{3} + 3 (x^{2}) (3)]$
$= 2 (27 + 9 x^{2}) = 18 x^{2} + 54$

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