Question

What is the coefficient of a^8b^2 in the expansion (1/3a^2 - 4b)^6​

Answer 1

Explanation:

(1/3a^2-4b)^6 for such an expansion the general term is

`tr + 1 = \binom{6}{r} * ( (1)/(3) {a}^(2) ) ^(6 - r) * (4b)^(r)`

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