Question

expand sin^4(x)

Answer 1

(sinx)^2 + cos(x)^2 = 1 //basic trig identity
(sinx)^4 => ((sinx)^2) * ((sinx)^2) //breaking it down
(sinx)^2 = 1 - (cosx)^2 //rearranging trig identity
therefore;
(sinx)^4 = (1 - (cosx)^2)^2
Use foil to factor out.

Answer 2

but it has to be expanded to the point where it doesnt have exponents

Answer 3

using half-angle identities to simplify it down into powers of 1I get:
(1/3) - (2/3)cos(2x) + (cos2x)/3

Answer 4

how did you get to that?

Answer 5

I messed up somewhere looking back.
it's very long, so I didn't want to type it out.
(sinx)^4 = ((sinx)^2) * ((sinx)^2) //stated before, pretty obvious
(sinx)^2 = (1-cos2x)/2 // half-angle identity
therefore:
(sinx)^4 = (1/4)(1- cos2x)^2 //substitution and factoring stuff out
(sinx)^4 = (1/4)(1 -2cos2x + (cos2x)^2) //FOIL
4(sinx)^4 = 1 - 2cos2x + (1 +cos4x)/2 //half-angle identity on the last term
(sinx)^4 = 1/4 - (1/2)cos2x + (1 + cos4x)/8 //divide by 4