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nth Term of A.P

Simplify: 2...

Question

Simplify: $(2 x + 3)^{3} - (2 x - 3)^{3}$
Answer: $54 + 72 x^{2}$

A

True

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B

False

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Solution

The correct option is A True
$(2 x + 3)^{3} - (2 x - 3)^{3}$
$= (2 x)^{3} + 3^{3} + 3. (2 x)^{2} .3 + 3.2 x {.3}^{2} - [(2 x)^{3} - 3^{3} - 3. (2 x)^{2} .3 + 3.2 x {.3}^{2}]$
$= (2 x)^{3} - (2 x)^{3} + 3^{3} + 3^{3} + 3. (2 x)^{2} .3 + 2.3.2 x {.3}^{2} - 3.2 x {.3}^{2}$
$= 54 + 72 x^{2}$

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