For a positive integer $n,$ simplify
\[1^2 - 2^2 + 3^2 - 4^2 + \dots + (2n - 1)^2 - (2n)^2.\]
Question:
For a positive integer $n,$ simplify
\[1^2 - 2^2 + 3^2 - 4^2 + \dots + (2n - 1)^2 - (2n)^2.\]
Answer:
Let's think step by step.

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