What is the factorised form of (12a^2-17ab+6b^2)?

Correct answer: ((3a-2b)(4a-3b))

The direct answer is A: \((3a-2b)(4a-3b)\). Multiply the leading terms: \(3a\cdot4a=12a^2\), and the constants give \((-2b)(-3b)=6b^2\). The cross terms are \(-9ab\) and \(-8ab\), whose sum is \(-17ab\). Thus the product is exactly \(12a^2-17ab+6b^2\). Option A is correct. Option B gives leading coefficient \(12a^2\) but cross terms \(-36ab-2ab=-38ab\), so it fails. Option C expands to \(12a^2-18ab+6b^2\), not the required middle term. Option D gives positive cross terms, so the sign is wrong. Check the product, sum, and signs of the split middle terms.