To simplify the expression we need to apply the trigonometric identities for cosine and sine of a sum or difference of angles:

cos(2a) = cos^2(a) - sin^2(a)
cos(-a) = cos(a)
sin(-a) = -sin(a)
sin(-2a) = -2sin(a)cos(a)

Now we can substitute these identities into the expression:

cos(2a) - cos(-a)sin(-2a)
= (cos^2(a) - sin^2(a)) - (cos(a))(-2sin(a)cos(a))
= cos^2(a) - sin^2(a) + 2sin(a)cos^2(a)
= cos^2(a) - sin^2(a) + 2cos(a)sin(a)cos(a)
= cos^2(a) - sin^2(a) + 2cos^2(a)sin(a)
= cos^2(a) - sin^2(a) + 2cos^2(a)sin(a)
= cos^2(a) - sin^2(a) + 2cos^2(a)sin(a)

Therefore, the simplified expression is cos^2(a) - sin^2(a) + 2cos^2(a)sin(a).