What is the factorised and simplified form of ((x+y)^2-(x-y)^2)?

Correct answer: (4xy)

The direct answer is option A: \(4xy\). Use the difference-of-squares identity with \(A=x+y\) and \(B=x-y\): \(A^2-B^2=(A-B)(A+B)\). Now \(A-B=(x+y)-(x-y)=2y\), and \(A+B=(x+y)+(x-y)=2x\). Their product is \(2y\cdot2x=4xy\). Option A is therefore correct. Option B is too small by a factor of two. Option C, \(x^2-y^2\), is the result of a different expression and does not account for both given squares. Option D gives the sum-like result \(2x^2+2y^2\), because it incorrectly treats the cross terms as if they had the same sign. Memory cue: subtracting the conjugate squares leaves four times the product.