Calculating of roots of unity

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$$P(x) = (x-1)(x-\omega_{15})(x-\omega_{15}^2)...(x-\omega_{15}^{14})$$

Where $\omega$ is a root of unity of order 15 and $\omega_{15}= e^{2\pi i/15}$

I need to simplify this.

The solution is using fast fourier transform but I am not able to simplify it. The only lead I have is that 2 polynomials of same degree which have the same coefficient in front of the largest power and have same zeros are equal.

Any ideas on how to approach this problem?