SAT Question f89e1d6f: Equivalent Expressions answer and explanation with Desmos solution

Choice C is correct. Factoring $-1$ from the second, third, and fourth terms gives $x^2-c^2-2cd-d^2=x^2-(c^2+2cd+d^2)$. The expression $c^2+2cd+d^2$ is the expanded form of a perfect square: $c^2+2cd+d^2=(c+d{)}^2$. Therefore, $x^2-(c^2+2cd+d^2)=x^2-(c+d{)}^2$. Since $a=c+d$, $x^2-(c+d{)}^2=x^2-a^2$. Finally, because $x^2-a^2$ is the difference of squares, it can be expanded as $x^2-a^2=(x+a)(x-a)$.