Luke notices that by taking any three consecutive integers, multiplying them together, and adding the middle number to the result, the answer always seems to be the middle number cubed.
For example:
3.4.5+ 4 = 64 = 43
4.5.6 +5 = 125 = 53
9. 10. 11 + 10 = 1000 = 103
a. To prove his observation, Luke writes (n + 1)(n+2)(n+3) + (n + 2). What answer is he hoping
to show this expression equals?