Advanced Math practice question

Answer: A. 3xy(2x − 3y)

The greatest common factor of 6x²y and 9xy² is 3xy. Dividing each term by it: 6x²y / 3xy = 2x and 9xy² / 3xy = 3y. So the expression is 3xy(2x − 3y).

Why the other answers are wrong

B. 3xy(2x − 3)

After factoring out 3xy, the second term is 9xy² / 3xy = 3y, not 3. The y didn't fully come out.

C. 3xy(2x − 3y²)

3xy(2x − 3y²) expands to 6x²y − 9xy³ — the second term has y cubed. Dividing 9xy² by 3xy leaves 3y, not 3y².

D. 3x(2xy − 3y)

3x(2xy − 3y) expands to 6x²y − 9xy: the second term lost a y. Both terms share a y, so it belongs in the common factor.

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