(x^2+2x+1)(x^2-2x+1)

Question

can someone teach me step by step on this?
do i foil the whole thing?

Answer 1

Are you supposed to expand it or factor it?

It factors into (x+1)^2(x-1)^2

That can also be written
[(x+1)(x-1)]^2 = (x^2-1)^2

which can be multiplied out right way (with FOIL) to give
x^4 -2x^2 +1

You can get the same answer by multiplying (x^2+2x+1) by each of the terms in
x^2 -2x +1
and adding up the results. Many terms would have canceled.

Answer 2

im supposed to expand it

Answer 3

I did, using a shortcut, and gave you the answer.

Answer 4

thank you :)