Step-by-step explanation:
(1/3a^2-4b)^6 for such an expansion the general term is
[tex]tr + 1 = \binom{6}{r} \times ( \frac{1}{3} {a}^{2} ) ^{6 - r} \times (4b)^{r} [/tex]
we want b^2 so r=2
so the formula transform to:
C6,2*(1/3)^4*a^8*4^2*b^2 so the coefficient of a^8b^2 is
(6*5/2*1)*(1/3^4)*4^2=
6*5*4*4/2*3*3*3*3=16*5/27=80/27
