Solve
$(2 a + 3 b) (2 a - 3 b) (4 a^{2} + 9 b^{2}) = ?$

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Solution

Using the identity $(a + b) (a - b) = a^{2} - b^{2}$ , the given expression can be written as:
$(2 a + 3 b) (2 a - 3 b) (4 a^{2} + 9 b^{2})$ $= (4 a^{2} - 9 b^{2}) (4 a^{2} + 9 b^{2})$
$= (4 a^{2})^{2} - (9 b^{2})^{2}$
$= 16 a^{4} - 81 b^{4}$ .

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