What is the complete common-factor form of (15a^2b − 10ab^2)?

Correct answer: 5ab(3a − 2b)

The correct answer is A: 5ab(3a − 2b). To factor by the common-factor method, first compare the terms 15a^2b and −10ab^2. The greatest common numerical factor of 15 and 10 is 5. Both terms contain a, and both contain b, so the greatest common factor is 5ab. Divide each term by 5ab: 15a^2b ÷ 5ab = 3a, and −10ab^2 ÷ 5ab = −2b. Therefore, the expression becomes 5ab(3a − 2b). Option A is correct because multiplying back gives 15a^2b − 10ab^2. Option B is not the complete common-factor form because it leaves an extra b inside the bracket and does not represent the original expression correctly when expanded. Option C gives 10a^2b − 10ab^2, so its first term is wrong. Option D gives 15a^2b − 30ab^2, so its second coefficient is wrong. Memory cue: take the smallest power of every variable common to all terms, then divide each term carefully.