If (3a+6b+c+2d)\times(3a-6b-c+2d)=(3a-6b+c-2d)\times(3a+6b-c-2d), then which one of the following is <strong>CORRECT</strong>?

Explanation

Let X = 3a+2d and Y = 6b+c. The left side is (X+Y)(X-Y) = X^2 - Y^2. Let U = 3a-2d and V = 6b-c. The right side is (U+V)(U-V) = U^2 - V^2. So, (3a+2d)^2 - (6b+c)^2 = (3a-2d)^2 - (6b-c)^2. Rearranging: (3a+2d)^2 - (3a-2d)^2 = (6b+c)^2 - (6b-c)^2. Expanding yields 4(3a)(2d) = 4(6b)(c) \implies 24ad = 24bc \implies ad=bc.

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