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=4^3, 4.5.6+5=125=5^3, 9.10.11+10=1000=10^3. use lulu’s expression to prove that adding the middle number to the product of any three consecutive numbers is sure to equal that middle number cubed.