Question

Factor. Assume variables in exponents represent positive integers.
a^16 - 1

Answer 1

(a-1)(a+1)(a^2+1)(a^4+1)(a^8+1)

Answer 2

is that the answer

Answer 3

yes do you understand?

Answer 4

no

Answer 5

okay. you can think of it like this. When you are given x^2-1, you can factor out to (x-1)(x+1), right?

Answer 6

right!

Answer 7

Okay. I know many people get scared when they see the higher exponents, but you can think of it same as ^2.

Answer 8

so a^16-1 => (a^8-1)(a^8+1)

Answer 9

you can't factor out a^8+1 so you leave it like that. now you have to work on a^8-1.
That one is going to be factored as (a^4-1)(a^4+1).

Answer 10

you can't factor our (a^4+1), so you leave it, and now, (a^4-1) becomes (a^2-1)(a^2+1)

Answer 11

and finally, when you leave (a^2+1) as it is, (a^2-1) becomes (a-1)(a+1).

Answer 12

so the final answer is (a-1)(a+1)(a^2+1)(a^4+1)(a^8+1)

Answer 13

thank you helped so much

Answer 14

no prob :)