Hi Lisa.

Use your inductive assumption.

You want to see if the statement is true for

.

Well you seem to have correctly observed that the expression for

is just the expression for

with

added on.

Since by inductive hypothesis, 16 divides the expression for

, all you have to do is verify that 16 divides

.

Expand this and you will see every term is divisible by 16. (you may find it easy to expand if you take advantage of its form as a difference of squares).

In your proof, you might want to explain that if a number (16) divides two numbers, then it divides their sum as well. Presumably, this property has been discussed/proved in your class or textbook by now, so just mentioning the fact will probably suffice.