Which is the factorisation of \(x^2-25\)?

Correct answer: \((x-5)(x+5)\)

Answer: C, \((x-5)(x+5)\). Rewrite 25 as \(5^2\), so the expression becomes \(x^2-5^2\). This is a difference of squares. Applying \(a^2-b^2=(a-b)(a+b)\) with a=x and b=5 gives \((x-5)(x+5)\). Expanding confirms it: \(x^2+5x-5x-25=x^2-25\). Option A is wrong because its product is \(x^2-24x-25\), not the given expression. Option B gives \(x^2+10x+25\), because it is a square of a sum. Option D gives \(x^2-10x+25\), because it is a square of a difference. Both B and D contain a middle term, whereas the original expression has none. Memory cue: for a difference of squares, use the square root of the constant and write one sum factor and one difference factor.