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Compute the sum \((a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + \cdots + (a+d)^2 - a^2\).

 

So I think I will have to apply difference of squares to this. But the many variables are confusing me and making it harder for me. I don't quite get the "2n+1, 2n, 2n-1 etc" part so it's making it difficult to factor. Can somone explain how this is factored step by step? I'd really appreciate it, thank you.

 Jun 23, 2020
edited by gwenspooner85  Jun 23, 2020
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This has been posted before and was solved, I believe. Search for it !.

 Jun 23, 2020
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I know, I did see it, but the person who answered it simply gave the answer only. I had no idea how they got it so I want a step by step explanation. Can anybody else help me?

 Jun 23, 2020

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