Once you find the GCF, rewrite the expression as (GCF)$\times$(something). Divide each term by the GCF to figure out what goes in the parentheses.

After factoring, compare the GCF and the binomial you found with each answer option. Which option has the same outside factor and the same two terms inside the parentheses, including signs?

In Desmos, type something like a=2 and b=1 (or any simple nonzero values) so that Desmos treats $a$ and $b$ as specific numbers.

Type E = 9a^2*b - 12a*b^2 so Desmos gives you a numerical value for the original expression using your chosen $a$ and $b$.

Type four more lines: A = 3a*b*(a - 4b), B = 3a*b*(3a - b), C = 9a*b*(a - 4b), and D = 3a*b*(3a - 4b). Compare the values of A, B, C, and D to the value of E.

If more than one choice matches for your first $(a,b)$, change a and b to different values (for example, a=3, b=-2) and check again. The correct expression will match the original every time; any incorrect choice will eventually give a different result.

Look at $9a^2b$ and $-12ab^2$:

• The GCF of the coefficients $9$ and $12$ is $3$.
• Each term has at least one $a$, so the GCF for $a$ is $a^1 = a$.
• Each term has at least one $b$, so the GCF for $b$ is $b^1 = b$.

So the greatest common factor of the whole expression is $3ab$.

Now divide each term by $3ab$ to see what will go inside the parentheses:

• $9a^2b / 3ab = 3a$
• $-12ab^2 / 3ab = -4b$

So, after factoring out $3ab$, the expression becomes $3ab$ times a binomial with terms $3a$ and $-4b$.

Putting the GCF and the binomial together, the expression becomes

Compare this with the answer choices: it matches $3ab(3a - 4b)$, which is the correct equivalent expression.