Question

Find the indicated term in the expansion of the given binomial.
The term that does not contain x in the expansion of

(6x+1/2x)^12

Is there an easier way to find the answer instead of going through finding 13 terms

Thanks.

Answer 1

When 'x' is not in the term, than x will have the same power in the numerator and denominator, and will hence cancel out.

So, (6x) and (1/2x) will be raised to same power.

Which term will this happen in?

Answer 2

(a+b)^12
where is power of a same as of b
C(12,6) a^6 b^6
where b is binomial coef
C(12,6) = 12!/[6! 6!] = 12*11*10*9*8*7/6!
=2*11*3*2*7
=924
so
924[(6x)^6 * 1/(2x)^6 ]
924 * 6^6/2^6

Answer 3

the 11th term? x can't be cancelled

Answer 4

Thanks Damon

Answer 5

the "center or middle" term ... 7th