Answer
$21-4\sqrt{5}$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial and the properties of radicals, the expression $
\left( 2\sqrt{5}-1 \right)^2
$ is equivalent to
\begin{array}{l}
\left( 2\sqrt{5} \right)^2+2\left( 2\sqrt{5} \right)(-1)+(-1)^2
\\\\=
4\cdot5-4\sqrt{5}+1
\\\\=
20-4\sqrt{5}+1
\\\\=
21-4\sqrt{5}
.\end{array}
