Let $a,$ $b,$ $c,$ and $d$ be real numbers such that $a^2 + b^2 = 8$ and $c^2 + d^2 = 13.$  Find
\[(ad - bc)^2 + (ac + bd)^2.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c,$ and $d$ be real numbers such that $a^2 + b^2 = 8$ and $c^2 + d^2 = 13.$  Find
\[(ad - bc)^2 + (ac + bd)^2.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
104
Let $a,$ $b,$ $c,$ and $d$ be real numbers such that $a^2 + b^2 = 8$ and $c^2 + d^2 = 13.$  Find
\[(ad - bc)^2 + (ac + bd)^2.\]
train