Question

simplify \left(2\sqrt{2}-\sqrt{3}\right)\left(2\sqrt{2}+\sqrt{3}\right)

Answers

GPT 3.5
Using the difference of squares pattern, we have $(a-b)(a+b)=a^2-b^2$ for any real numbers $a$ and $b$. In this case, $a = 2\sqrt{2}$ and $b = \sqrt{3}$. So we have \begin{align*}
(2\sqrt{2}-\sqrt{3})(2\sqrt{2}+\sqrt{3}) &= (2\sqrt{2})^2 - (\sqrt{3})^2 \\
&= 4\cdot 2 - 3 \\
&= \boxed{5}.
\end{align*}