Answer
$16k^2+8hk+h^2-32k-8h+16$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
[(4k+h)-4]^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(4k+h)^2+2(4k+h)(-4)+(-4)^2
\\\\=
(4k+h)^2-8(4k+h)+16
\\\\=
(4k+h)^2-32k-8h+16
\\\\=
[(4k)^2+2(4k)(h)+(h)^2]-32k-8h+16
\\\\=
16k^2+8hk+h^2-32k-8h+16
.\end{array}
