Answer
$49-8\sqrt{3}$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression $
\left( 4\sqrt{3}-1 \right)^2
$ simplifies to
\begin{array}{l}
\left( 4\sqrt{3} \right)^2+2\left( 4\sqrt{3} \right)(-1)+(-1)^2
\\\\=
16\cdot3-8\sqrt{3}+1
\\\\=
48-8\sqrt{3}+1
\\\\=
49-8\sqrt{3}
.\end{array}
