For which expression is the identity for the difference of two perfect squares most appropriate for factorisation?

Correct answer: \(25a^2-49b^2\)

The direct answer is B: \(25a^2-49b^2=(5a)^2-(7b)^2\). The difference-of-squares identity is \(A^2-B^2=(A-B)(A+B)\). Therefore B factorises as \((5a-7b)(5a+7b)\). Option A is \((3p-4)^2\), a perfect-square trinomial, so the difference-of-squares identity is not the most appropriate first method. Option C is a quadratic trinomial; it can be factorised by finding two numbers with product 10 and sum 7, not by the difference-of-squares identity. Option D is a sum of cubes, because \(8m^3=(2m)^3\) and \(27n^3=(3n)^3\); it belongs to a different identity. A useful warning is that the signs matter: the identity needs subtraction between two complete squares, not addition. Look for two square terms separated by a minus sign before applying the formula.