SAT Question a255ae72: Equivalent Expressions answer and explanation with Desmos solution

Choice B is correct. It's given that $x^2=a+b$ and $y^2=a+c$. Using the distributive property, the expression $(x^2-y^2{)}^2$ can be rewritten as $(x^2{)}^2-2x^2\times y^2+(y^2{)}^2$. Substituting $a+b$ and $a+c$ for $x^2$ and $y^2$, respectively, in this expression yields $(a+b{)}^2-2\times ((a+b)\times (a+c))+(a+c{)}^2$. Expanding this expression yields $(a^2+2ab+b^2)-(2a^2+2bc+2ac+2ab)+(a^2+2ac+c^2)$. Combining like terms, this expression can be rewritten as $b^2-2bc+c^2$.