Answer
$13$
Work Step by Step
Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the given expression, $
(4+\sqrt{3})(4-\sqrt{3})
,$ is equivalent to
\begin{align*}
&
(4+\sqrt{3})(4-\sqrt{3})
\\&=
(4)^2-(\sqrt{3})^2
\\&=
16-3
\\&=
13
.\end{align*}
Hence, the given expression simplifies to $
13
$.
