Question 12·Easy·Advanced Math

The largest number dividing both $12$ and $18$ is $6$. Both terms contain at least $m^2$ and $n$, so the greatest common factor, the largest factor shared by both terms, is $6m^2n$. You can't take out $m^3$ or $n^2$: each appears in only one term.

Divide the first term by the shared factor:

Taking two $m$ factors out of $m^3$ leaves one $m$.

Divide the second term by the same factor:

Only one $n$ remains inside because one $n$ is already in the shared factor.

Choose $m=2$ and $n=2$ for a numerical check. Using $1$ could hide a missing power because $1^2=1$. Type those values and the original expression into Desmos; it shows $480$.

The two quotients go inside the parentheses. Type $6m^2n(2m+3n)$ below the original in Desmos; it also shows $480$. That checks the arithmetic, while dividing both original terms by $6m^2n$ shows why the expressions match for any $m$ and $n$:

Choice D.