Question

What's the answer to both when simplifying the two radical expression?

Answer 1

$( \sqrt{x} +2 \sqrt{5})*( \sqrt{x} -2 \sqrt{5}) = \\ \\ ( \sqrt{x})^2- (\sqrt{x} *2 \sqrt{5})+(2 \sqrt{5}* \sqrt{x}) -(2 \sqrt{5})^2 = \\ \\ x- 2\sqrt{5} \sqrt{x}+2 \sqrt{5} \sqrt{x} -(4*5)= \\ \\ x -(4*5)= \boxed{x-20}$

$( \sqrt{x}+ \sqrt{5}) ^2= \\ \\ ( \sqrt{x})^2+2* \sqrt{x}* \sqrt{5} + (\sqrt{5}) ^2= \\ \\ \boxed{ x +2 \sqrt{5x}+5}$