Choose the correct factorisation of (p^2-q^2-5p+5q).

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

Direct answer: Option B, (p-q)(p+q-5). First use p²-q²=(p-q)(p+q). The remaining terms are -5p+5q=-5(p-q), because factoring out -5 from -5p+5q leaves p-q. Thus the expression becomes (p-q)(p+q)-5(p-q). Taking the common factor (p-q) gives (p-q)(p+q-5). Option A has p+q as the common factor, but the linear terms are not divisible by p+q in this way. Option B reproduces p²-q²-5p+5q when expanded. Option C gives +5p-5q after expansion, so both signs are wrong. Option D is algebraically the same product as A, and is therefore also wrong. Memory cue: first factor the difference of squares, then factor the common (p-q) from the last two terms.