Answer
${\bf (i-j)}\times{\bf (i+j)}={\bf 2k}$
Work Step by Step
${\bf (i-j)}\times{\bf (i+j)}=\left|\begin{array}{rrr}
{\bf i} & {\bf j} & {\bf k}\\
1 & -1 & 0\\
1 & 1 & 0
\end{array}\right|$
$=(0-0){\bf i}-(0-0){\bf j}+(1-(-1)){\bf k}$
$=2{\bf k}$
