Okay, I'm trying to simplify a trigonometric thing. I say "thing" because it's not an equation, and that has me a little confused.

Beginning: $\displaystyle 2 sinx cosx - 4 sin^{3}x cosx$

So, I'm not given what that is equal to, but told to factor and simplify. I looked up the answer, and they gave me the last two steps.

Second-to-last: $\displaystyle (2 sinx cosx) (1 - 2sin^{2}x)$

Last: $\displaystyle (sin2x) (cos2x)$

Okay, getting from the second-to-last step to the last is easy, using the double-angle formulae. I just don't know how to get from the beginning to the second-to-last step! I checked it out in MS Excel, and

$\displaystyle 2 sinx cosx - 4sin^{3}x cosx$ does in fact equal $\displaystyle (2 sinx cosx) (1 - 2sin^{2}x)$

... I just don't know how they got there. Is it that there is some common factor in the first two terms of the original thing? Can I divide each side of a subtraction operation in half or something?