Multiply and simplify, if possible. All variables represent positive real numbers. $( \sqrt { 5 m } + \sqrt { 2 n } ) ( \sqrt { 5 m } - \sqrt { 2 n } )$
A) $5 m - 2 n$
B) $5 n - 2 m$
C) $- 5 m - 2 n$
D) $5 m + 2 n$
E) $- 5 m + 2 n$

Question

Quizplus · Accepted Answer

This problem uses the difference of squares formula, $a^2 - b^2 = (a + b)(a - b)$. Here, $a = \sqrt{5m}$ and $b = \sqrt{2n}$, so the expression simplifies to $(\sqrt{5m})^2 - (\sqrt{2n})^2 = 5m - 2n$.

Multiply and Simplify, If Possible (5m+2n)(5m−2n)( \sqrt { 5 m } + \sqrt { 2 n } ) ( \sqrt { 5 m } - \sqrt { 2 n } )(5m​+2n​)(5m​−2n​)

Multiply and Simplify, If Possible $( \sqrt { 5 m } + \sqrt { 2 n } ) ( \sqrt { 5 m } - \sqrt { 2 n } )$