Simplify the following expression. \((2x + 3y)^{2} - (2x - 3y)^{2} + 12xy\)
\(36xy\)
Use the identity \(a^{2} - b^{2} = (a+b)(a-b)\).
Here \(a = 2x + 3y\) and \(b = 2x - 3y\), so \(a + b = 4x\) and \(a - b = 6y\).
Therefore \((2x+3y)^{2} - (2x-3y)^{2} = 4x \times 6y = 24xy\).
Adding the remaining term: \(24xy + 12xy = 36xy\).
Hence, the simplified value of the expression is \(36xy\).
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