Choose the factorised form of \(p^2-25q^2\).

Correct answer: \((p-5q)(p+5q)\)

The direct answer is A: \((p-5q)(p+5q)\). Rewrite the second term as a square: \(25q^2=(5q)^2\). The expression is therefore \(p^2-(5q)^2\), which matches \(a^2-b^2=(a-b)(a+b)\), with \(a=p\) and \(b=5q\). Hence the factorisation is \((p-5q)(p+5q)\). Option B does not use the correct square root of \(25q^2\) and expands to unrelated terms. Option C is a square of a sum; its expansion contains a positive middle term \(10pq\). Option D is a square of a difference; its expansion contains a negative middle term \(-10pq\). The original expression has no \(pq\) term, because the cross terms must cancel. Memory cue: in a difference of squares, keep the same terms but use opposite signs in the two brackets.