FP1 Summations

4*sum(r^2) - 4*sum(r) + sum(1)

sum r^2 = n/6(n+1)(2n+1)
sum r = n/2(n+1)
sum 1 = n

Find
n
∑(2r − 1)^2, expressing your answer in a fully factorised form.
r=1

Sorry about the format

I was able to simplify it down as shown and substitute in the summations for each r but I haven't been able to simplify it down to the answer.

Did you factor out (n+1) and (n) ?

4n/6(n+1)(2n+1) - 4n/2(n+1) + n

4n/6(n+1)(2n+1) - 12n/6(n+1) +6n/6

n/6(4(n+1)(2n+1) - 12(n+1) + 6)

n/6((n+1)(4(2n+1) -12) + 6)

n/6((n+1)(8n-8) + 6)

n/6(8n^2 - 8n + 8n - 8 + 6)

n/6(8n^2 - 2)

2n/6(4n^2 - 1)

2n/6(2n+1)(2n-1)

(1/3)(n)(2n+1)(2n-1)

You can do it a lot quicker, but I was just including all the steps. You should end up with something like that.