What is obtained by taking out the common factor from \(12p^2q-8pq^2\)?

Correct answer: \(4pq(3p-2q)\)

The direct answer is B: \(4pq(3p-2q)\). Find the greatest common factor by considering numbers and variables separately. The greatest common numerical factor of 12 and 8 is 4. Both terms contain p and q; the smallest powers common to both are p and q, so the variable part is pq. Thus the greatest common factor is \(4pq\). Divide: \(12p^2q\div4pq=3p\), and \(-8pq^2
div4pq=-2q\). Hence \(12p^2q-8pq^2=4pq(3p-2q)\). Option A is algebraically equivalent because it expands to the same expression, but it does not remove the greatest common factor; 2pq is not the greatest possible common factor. Option C does not reproduce the terms and has an incorrect coefficient. Option D is also algebraically equivalent to the original expression, but it leaves q inside and therefore does not take out the full common factor. Option B is the expected fully factorised form. Always multiply back to check both terms and signs.