Aflorist needs several pieces of ribbon that are 5 and 1/2 inches long if she begins with a piece of ribbon that is 264 inches long how many pieces will she be able to cut from it

  48

Step-by-step explanation:

(264 in)/(5.5 in/piece) = (264/5.5) pieces = 48 pieces

Division is the usual shortcut for repeated subtraction. You could subtract 5.5 from 264 until you get to zero. You would have to do 48 subtractions. It is easier to divide 264 by 5.5 to see how many times it goes.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18