Multiply, then simplify the product. Assume that all variables represent positive real numbers.
-$(4 \sqrt{x}+\sqrt{y})(4 \sqrt{x}-\sqrt{y})$
A) $16 x-y$
B) $16 x^{2}-y^{2}$
C) $16 x-2 \sqrt{x y}-y$
D) $16 x+y$

Question

Quizplus · Accepted Answer

This is an application of the difference of squares formula, $a^2 - b^2 = (a+b)(a-b)$. Here, $a = 4\sqrt{x}$ and $b = \sqrt{y}$, so the product simplifies to $(4\sqrt{x})^2 - (\sqrt{y})^2 = 16x - y$.

Multiply, Then Simplify the Product (4x+y)(4x−y)(4 \sqrt{x}+\sqrt{y})(4 \sqrt{x}-\sqrt{y})(4x​+y​)(4x​−y​) A) 16x−y16 x-y16x−y B) 16x2−y216 x^{2}-y^{2}16x2−y2

Multiply, Then Simplify the Product $(4 \sqrt{x}+\sqrt{y})(4 \sqrt{x}-\sqrt{y})$ A) $16 x-y$ B) $16 x^{2}-y^{2}$