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.