cos(2alpha)cos(alpha) + cos(alpha) + sin(alpha)sin(2alpha)

Expanding cos(2alpha) using the double angle identity:

(2cos(alpha)^2 - 1)cos(alpha) + cos(alpha) + sin(alpha)2sin(alpha)*cos(alpha)

Apply trigonometric identities:

2cos(alpha)^3 - cos(alpha) + cos(alpha) + 2sin(alpha)^2*cos(alpha)

Simplify further:

2cos(alpha)^3 + cos(alpha) + 2sin(alpha)^2*cos(alpha)

Can be simplified to:

cos(alpha)(2cos(alpha)^2 + sin(alpha)^2 + 1)