For a positive integer $n,$ simplify
\[1^2 - 2^2 + 3^2 - 4^2 + \dots + (2n - 1)^2 - (2n)^2.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For a positive integer $n,$ simplify
\[1^2 - 2^2 + 3^2 - 4^2 + \dots + (2n - 1)^2 - (2n)^2.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-2n^2 - n
For a positive integer $n,$ simplify
\[1^2 - 2^2 + 3^2 - 4^2 + \dots + (2n - 1)^2 - (2n)^2.\]
train