How do I factorise to get from this line ..... to this line?

Question

how do I factorise the top line to get the bottom?

$1 + 2p(1 − \cos(\omega)) + p^2(2 − 2 \cos(\omega))$

$= 1 + 2p(1 + p)(1 − \cos(\omega))$

thanks for your help :)

Answer 1

$p^2(2 - 2 \cos \omega) = 2 p (1 - \cos \omega) \cdot p$. Then undistribute the common factor, $ 2 p (1 - \cos \omega)$.

Answer 2

Using $$\sin^2(x)+\cos^2(x)=1$$ we get $$1+2p(1-\cos(\omega)+2p^2(1-\cos(\omega))=1+2(1-\cos(\omega))(p+p^2)=1+2p(1-\cos(\omega))(1+p)$$