If ( (x+y)^2-(x-y)^2=72 ), what is the value of (xy)?

Correct answer: (18)

The direct answer is B, 18. Apply \\((x+y)^2-(x-y)^2=4xy\\). The question says the difference is 72, so \\(4xy=72\\). Dividing both sides by 4 gives \\(xy=18\\). Option A, 12, would make the difference 48, not 72. Option B is correct because 4 multiplied by 18 is 72. Option C, 24, would give 96. Option D, 36, would give 144. The important step is to simplify the whole difference before trying to find x and y separately; only their product is requested. This identity follows because the x-squared and y-squared terms cancel, while the two middle contributions add. Memory cue: plus-square minus minus-square equals four times the product.