(1)
a.b = |a||b|cos120°= -4
(2)
|a+b|^2= |a|^2+|b|^2+2|a||b|cos120°=16+4-8=12
(3)
|a|^2-|b|^4=16-16=0
(4)
(a-2b).(a+b)
=|a|^2-2|b|^2-|a||b|cos120°
=16-8+4
=8