Find the product of $(2 a + 3) (2 a - 3) (4 a^{2} + 9)$

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Solution

Using the formula $(a + b) (a - b)$ = $a^{2} - b^{2}$
$(2 a + 3) (2 a - 3) = (2 a)^{2} - (3)^{2}$
$= 4 a^{2} - 9$
$⟹ (4 a^{2} - 9) (4 a^{2} + 9) = (4 a^{2})^{2} - (9)^{2}$
$= 16 a^{4} - 81$

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