Answer
$6+2\sqrt{6}-2\sqrt{2}-2\sqrt{3}$
Work Step by Step
Using $(a+b+c)=a^2+b^2+c^2+2ab+2ac+2bc$ (or the square of a multinomial), the given expression, $
(\sqrt{2}+\sqrt{3}-1)^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{2})^2+(\sqrt{3})^2+(-1)^2+2(\sqrt{2})(\sqrt{3})+2(\sqrt{2})(-1)+2(\sqrt{3})(-1)
\\\\=
2+3+1+2\sqrt{2(3)}-2\sqrt{2}-2\sqrt{3}
\\\\=
6+2\sqrt{6}-2\sqrt{2}-2\sqrt{3}
.\end{array}
