Question 156·Easy·Advanced Math

Both $4y^2$ and $-12y$ contain $4y$: $4$ divides both coefficients, and each term has at least one $y$. So $4y$ is the greatest common factor. Divide each term by that factor to find what stays inside the parentheses:

Choose the nonzero value $y=2$ so a missing factor of $y$ won't disappear. Type $y_1=2$, then $4y_1^2-12y_1$ in Desmos. It gives $-8$ for the original expression.

Put the shared $4y$ outside and the quotients $y$ and $-3$ inside: $4y^2-12y=4y(y-3)$. Type $4y_1(y_1-3)$ on the next Desmos line; it also gives $-8$. That value checks the arithmetic, while factoring proves the match for every $y$. So $4y(y-3)$ is the equivalent expression. Choice D.