Choose the correct factorisation of (x²−2xy+y²).

Correct answer: (x−y)²

The direct answer is B: (x−y)². Use the identity A²−2AB+B²=(A−B)². Here A=x and B=y, so x²−2xy+y²=(x−y)². A step-by-step check is useful: the square of x gives x², the square of y gives y², and the middle term in (x−y)² is −2xy, exactly as required. Option A is incorrect because (x+y)²=x²+2xy+y²; its middle sign is positive. Option C uses the difference-of-squares identity and expands to x²−y², so it lacks the −2xy term. Option D expands to x²−3xy+2y², which does not match the original expression. A common confusion is to choose the sign from the first and last terms only; always check the middle term, since its sign determines whether the binomial is x+y or x−y.