What is the factorised form of \(ax+ay+bx+by\)?

Correct answer: \((a+b)(x+y)\)

The direct answer is A: \((a+b)(x+y)\). Use grouping: the first two terms have a common factor \(a\), and the last two have a common factor \(b\). Thus \(ax+ay+bx+by=a(x+y)+b(x+y)\). Now \((x+y)\) is common to both grouped terms, so take it outside: \((a+b)(x+y)\). Expanding this result gives \(ax+ay+bx+by\), confirming it. B expands to \(ab+ay+bx+xy\), which contains different terms. C expands to \(ab+ax+by+xy\), also not the original expression. D would give only \(abx+aby\), and it cannot produce the four required terms. A useful method is to group terms so that the same binomial appears twice; then factor out that common binomial.