Simplify: \((3\sqrt{5} + 2\sqrt{3})^{2} - (3\sqrt{5} - 2\sqrt{3})^{2}\).
\(24\sqrt{15}\)
Using the identity \((a+b)^2-(a-b)^2=4ab\) with \(a=3\sqrt5\) and \(b=2\sqrt3\):
\(4ab = 4 \times 3\sqrt5 \times 2\sqrt3 = 24\sqrt{15}\).
Hence, this is the correct answer., \(24\sqrt{15}\), is correct.
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