If $a^2 + b^2 = 3$ and $c^2 + d^2 = 4$, find the value of

$$(ac+bd)^2 + (bc - ad)^2.$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $a^2 + b^2 = 3$ and $c^2 + d^2 = 4$, find the value of

$$(ac+bd)^2 + (bc - ad)^2.$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
If $a^2 + b^2 = 3$ and $c^2 + d^2 = 4$, find the value of

$$(ac+bd)^2 + (bc - ad)^2.$$
train