Which expression can be factorised using only the identity for the difference of squares, \(a^2-b^2=(a-b)(a+b)\)?

Correct answer: \(x^2-25y^2\)

The correct answer is A: \(x^2-25y^2\). Rewrite \(25y^2\) as \((5y)^2\), so the expression is \(x^2-(5y)^2\). It has the exact form \(A^2-B^2\), with \(A=x\) and \(B=5y\). Therefore it factorises as \((x-5y)(x+5y)\). Option B is a sum of squares, not a difference, so the given identity does not apply. Option C is the perfect square \((x+5y)^2\) and is better handled by the square identity. Option D is the perfect square \((x-5y)^2\), not a difference of two separate squares in the required two-factor pattern. Expanding option A gives \(x^2+5xy-5xy-25y^2=x^2-25y^2\). Memory cue: look for a minus sign between two complete squares; the resulting factors are conjugates with opposite signs.