Which is the factorisation of (ab − ac + db − dc)?

Correct answer: (a + d)(b − c)

The correct answer is A: (a + d)(b − c). Begin by grouping terms that have a similar part: ab − ac + db − dc = (ab − ac) + (db − dc). Take the common factor from each group: a(b − c) + d(b − c). Now (b − c) is common to both terms, so take it outside: (a + d)(b − c). Verification is useful: multiplying gives ab − ac + db − dc, exactly the original expression. Option B gives ab − ac − db + dc, so the signs of the last two terms are wrong. Option C gives ab + ac + db + dc, so the signs involving c are wrong. Option D gives ab + ac − db − dc, which also has incorrect signs. Memory cue: group in pairs and preserve every sign; a common bracket must be identical in both groups.