Which is the correct factorised form of x² + 2xy + y² − 25?

Correct answer: (x + y − 5)(x + y + 5)

The direct answer is A: (x + y − 5)(x + y + 5). First recognise the initial three terms: x² + 2xy + y² = (x + y)². Also, 25 = 5². Thus the whole expression becomes (x + y)² − 5². Apply the difference-of-squares identity P² − Q² = (P − Q)(P + Q), with P = x + y and Q = 5. This gives (x + y − 5)(x + y + 5). Option B uses (x − y)², whose middle term would be −2xy. Option C does not have factors whose product gives the original terms. Option D changes subtraction into addition and is not a factorised product. Always identify the perfect square before applying the second identity.