The correct option is D None of the aboveWe know, #10; (a+b)^3=a^3+b^3+3a^2b+3ab^2 #10; #10;and #160; (a b)^3=a^3 b^3 3a^2b+3ab^2 .Then, (2 ...

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nth Term of A.P

2+3x3+2-3x3=?

Question

$(2 + 3 x)^{3} + (2 - 3 x)^{3}$ =?

16 + 54 x^{2}

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16 + 32 x^{2}

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16 + 27 x^{2}

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None of the above

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Solution

The correct option is D None of the above
We know, $(a + b)^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$

and $(a - b)^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$ .
Then,
$(2 + 3 x)^{3} + (2 - 3 x)^{3}$
$= (8 + 27 x^{3} + 36 x + 54 x^{2}) + (8 - 27 x^{3} - 36 x + 54 x^{2})$
$= 16 + 108 x^{2}$ .
(2+3x)3+(2−3x)3

Therefore, option $D$ is correct.

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