Answer
$9x^2+24x-6xy-8y+y^2+16$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ (or the Square of a binomial), the given expression, $
[4+(3x-y)]^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
4^2+2(4)(3x-y)+(3x-y)^2
\\\\=
16+24x-8y+(3x-y)^2
\\\\=
16+24x-8y+(3x)^2+2(3x)(-y)+(-y)^2
\\\\=
16+24x-8y+9x^2-6xy+y^2
\\\\=
9x^2+24x-6xy-8y+y^2+16
.\end{array}
