Factorise 81a^2 − 18ab + b^2.

Correct answer: (9a − b)^2

The correct answer is B: (9a − b)^2. Apply (p − q)^2 = p^2 − 2pq + q^2. Let p = 9a and q = b. Then p^2 = 81a^2, −2pq = −2(9a)(b) = −18ab, and q^2 = b^2. These are exactly the three terms in the given expression, so the factorisation is (9a − b)^2. Option A gives a positive middle term, 18ab, and therefore does not match. Option C has an incorrect first term: (81a)^2 is 6561a^2, not 81a^2. Option D expands using the difference-of-squares identity to 81a^2 − b^2, so it lacks the middle term. Common confusion: a negative middle term does not mean a difference of squares automatically; if there are three matching terms, check for the square of a difference first.