SAT Question dc67c130: Equivalent Expressions answer and explanation with Desmos solution

Choice D is correct. For the expression $64t^2{s}^3-56t^{3}s$, $4$ is a common factor of $64$ and $56$, $t^2$ is a common factor of $t^2$ and $t^3$, and $s$ is a common factor of $s^3$ and $s$. It follows that $4t^{2}s$ is a common factor of each term in the given expression. Factoring out $4t^{2}s$ from each term in the expression $64t^2{s}^3-56t^{3}s$ yields $4t^{2}s(16s^2-14t)$. Therefore, $4t^{2}s(16s^2-14t)$ is equivalent to $64t^2{s}^3-56t^{3}s$.