State whether the statement is True or False:
$(2 a + 3) (2 a - 3) (4 a^{2} + 9)$ is equal to $16 a^{4} - 81$ .

True

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False

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Solution

The correct option is A True
Given, $(2 a + 3) (2 a - 3) (4 a^{2} + 9)$ .

We know, $(a + b) (a - b)$ $= (a^{2} - b^{2})$ .

Multiply by using direct method, we get,
$(2 a + 3) (2 a - 3) (4 a^{2} + 9)$ $= [(2 a)^{2} - (3)^{2}] (4 a^{2} + 9)$
$= (4 a^{2} - 9) (4 a^{2} + 9)$ $= (4 a^{2} + 9) (4 a^{2} - 9)$ .
Now, by using formula $(a^{2} - b^{2}) = (a + b) (a - b)$ , we get,
$= ((4 a^{2})^{2} - (9)^{2})$
$= 16 a^{4} - 81$ .

Hence, the statement is true.
Therefore, option $A$ is correct.

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