Which algebraic identity is most suitable for factorising \(a^2-25\)?

Correct answer: \(x^2-y^2=(x-y)(x+y)\)

The direct answer is A: \(x^2-y^2=(x-y)(x+y)\). Rewrite 25 as \(5^2\), so \(a^2-25=a^2-5^2\). This is a difference of two squares, and the identity gives \(a^2-5^2=(a-5)(a+5)\). Option B is the identity for the square of a sum and is used for a three-term expression with a positive middle term. Option C is the identity for the square of a difference and also requires a three-term expression containing \(-2xy\). Neither applies directly to two squares separated by subtraction. Option D concerns a sum of cubes, but the expression contains squares, not cubes, and it is a difference rather than a sum. Option A is therefore the suitable identity, even though its letters x and y are general symbols; they can represent a and 5. Memory cue: two perfect squares with a minus sign between them signal difference of squares.