Answer
$9a^2+6ab+b^2-6a-2b+1$
Work Step by Step
Using $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the expression, $
[(3a+b)-1]^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3a+b)^2-2(3a+b)(1)+(1)^2
\\\\=
(3a+b)^2-6a-2b+1
\\\\=
(3a)^2+2(3a)(b)+(b)^2-6a-2b+1
\\\\=
9a^2+6ab+b^2-6a-2b+1
.\end{array}
