Question

Factor, the simplify.
sin^3(x)-sin^2(x)-sinx+1

Answer 1

\[\sin^2x(sinx-1)-1(sinx-1)\]

Answer 2

take sinx-1 out

Answer 3

and can that be simplified further?

Answer 4

= (sinx - 1)(sin^2 x - 1)

- now you can factor the second parentheses

Answer 5

- its the difference of 2 squares

Answer 6

the second parentheses would be sin(x) +1 * sin(x) -1

Answer 7

Yes :
So, finally you will get like:
\[(\sin(x) - 1)(\sin(x) + 1) (\sin(x)-1) \implies (\sin(x)-1)^2(\sin(x)+1)\]

Answer 8

thanks!

Answer 9

check the attachment