Factorise (3a^2-5ab-2b^2).

Correct answer: ((3a+b)(a-2b))

The direct answer is option A: \((3a+b)(a-2b)\). Multiply term by term: \(3a\cdot a=3a^2\), \(3a\cdot(-2b)=-6ab\), \(b\cdot a=ab\), and \(b\cdot(-2b)=-2b^2\). Combining the middle terms gives \(-6ab+ab=-5ab\), so the result is \(3a^2-5ab-2b^2\). Option A is exactly correct. Option B gives \(3a^2+6ab-ab-2b^2=3a^2+5ab-2b^2\), so the middle sign is wrong. Option C gives \(3a^2-2ab-b^2\), with both the middle and last coefficients wrong. Option D gives \(3a^2+3ab-2ab-2b^2=3a^2+ab-2b^2\), not the required middle term. Memory cue: always multiply all four pairs and combine only like terms.