SAT Mathematics Practice Test 5

The given equation can be thought of as the difference of two squares, where one square is${\mathit{x}}^2$ and the other square is ${\left(\sqrt{\mathit{a}}\right)}^2$ . Using the difference of squares formula, the equation can be rewritten as $\mathit{y}=\left(\mathit{x}+\sqrt{\mathit{a}}\right)\left(\mathit{x}-\sqrt{\mathit{a}}\right).$
Choices A, C, and D are incorrect because they are not equivalent to the given equation. Choice A is incorrect because it is equivalent to $\mathit{y}={\mathit{x}}^2-{\mathit{a}}^2$. Choice C is incorrect because it is equivalent to $\mathit{y}={\mathit{x}}^2-\frac{{\mathit{a}}^2}{4}$.Choice D is incorrect because it is equivalent to $\mathit{y}={\mathit{x}}^2+2\mathit{a}\mathit{x}+{\mathit{a}}^2$