Answer
$4h^2-4hk+k^2-j^2$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $
[(2h-k)+j][(2h-k)-j]
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2h-k)^2-(j)^2
\\\\=
(2h-k)^2-j^2
.\end{array}
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above is equivalent to
\begin{array}{l}\require{cancel}
[(2h)^2+2(2h)(-k)+(-k)^2]-j^2
\\\\=
4h^2-4hk+k^2-j^2
.\end{array}