What is the simplest factorised form of \(32m^2n-40mn^2\)?

Correct answer: \(8mn(4m-5n)\)

The direct answer is B: \(8mn(4m-5n)\). First find the greatest common factor. The numerical HCF of 32 and 40 is 8. Both terms contain m and n, and the lowest powers are m^1 and n^1, so the common factor is \(8mn\). Divide each term by it: \(32m^2n\div8mn=4m\), while \(-40mn^2\div8mn=-5n\). Thus \(32m^2n-40mn^2=8mn(4m-5n)\). A has the wrong sign and would produce a positive second term. C is an incomplete numerical factorisation; it expands to \(32m^2n-20mn^2\), not the original. D gives \(32m^2n-80mn^2\). B expands exactly to the given expression. A reliable habit is to multiply the outside factor by every term inside the bracket.