Choose the correct factorisation of \(x^2-2xy+y^2-25\).

Correct answer: \((x-y-5)(x-y+5)\)

Answer: A. First recognise the first three terms as a perfect square: \(x^2-2xy+y^2=(x-y)^2\). The whole expression is therefore \((x-y)^2-25=(x-y)^2-5^2\). Applying \(U^2-V^2=(U-V)(U+V)\), with \(U=x-y\) and \(V=5\), gives \((x-y-5)(x-y+5)\). Option B uses \((x+y)^2\), whose middle term would be +2xy, not −2xy. Option C is only a rewritten expression and also has the wrong sign before 25; the original has subtraction. Option D does not produce the required quadratic expression when multiplied. The important order is: identify the trinomial square first, then apply the difference-of-squares identity.