The coefficients of x^2x2 and x^3x3 in the expansion of (3-2x)^6(32x)6 are *a* and *b* respectively. Find the values of a/bab ?

The coefficients of x^2x2 and x^3x3 in the expansion of (3-2x)^6(32x)6 are a and b respectively. Find the values of a/bab .

1 Answer
Nov 25, 2017

The answer is =1.125=1.125

Explanation:

The binomial theorem is

(p+q)^6=((6),(0))p^6+((6),(1))p^5q+((6),(2))p^4q^2+((6),(3))p^3q^3+((6),(4))p^2q^4+((6),(5))pq^5+((6),(6))q^6

where,

((n),(k))=(n!)/((n-k)!(k!))

Here,

we have

p=3 and q=-2x

Therefore,

The coefficients of x^2 is

=((6),(2))3^4*(-2x)^2=(6!)/((6-2)!(2!))81*(4)x^2

=(6*5)/(1*2)*324x^2

a=4860

The coefficients of x^3 is

=((6),(3))3^3*(-2x)^3=(6!)/((6-3)!(3!))27*(-8)x^3

=-(6*5*4)/(1*2*3)*27*8x^3

b=-4320

Finally,

a/b=4860/(-4320)=-1.125