<s>[INST] Simplify $2(\sin^6x + \cos^6x) - 3(\sin^4 x + \cos^4 x) + 1$ Here is the expression:

$$2(\sin^6x + \cos^6x) - 3(\sin^4 x + \cos^4 x) + 1$$

The exercise is to evaluate it. 
In my text book the answer is $0$
I tried to factor the expression, but it got me nowhere.
 [/INST] Let $t=\sin^2(x)$.
$$2(t^3+(1-t)^3)-3(t^2+(1-t)^2)+1=6t^2-6t+2-6t^2+6t-3+1=0.$$
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