for this question first i identified (r+1)^2 = r^2+2r+1
i subbed in r+1 into r which gave me f(r+1)= 2r^3 + 8r^2 + 13r + 6
then subtracted the expanded version of f(r) which is 2r^3 + 3r^2 + r
which at the end gave me 5r^2 + 12r + 6
i think the 5 in my answer should be 6
spot my mistake please.
You are correct in your assumption.....
instead of 2 r^3 + 8r^2 + 13 r + 6 I get
2 r^3 + 9r^2 + 13r + 6 ....... So when you were expanding, you got something a little befuzzled.....look at it again....G'Luck !