Question

What is the second term in the binomial expansion of (2r – 3s)12? –73,728r11s 73,728r11s 608,256r10s2 –608,256r10s2?

Answer 1

It is A, my friend. I have taken the test and got it right ;)

Answer 2

Solution:

A is the correct option.

Explanation:

We have been given that $(2r - 3s)^{12}$

The $r^{th}$ term of a binomial expansion $(a+b)^n$ is given by

$t_r=^{n}C_{r-1}a^{n-r+1}b^{r-1}$

For the given binomial expansion, we have

$a=2r,b=-3s,r=2,n=12$

On plugging this value in the above formula, we have

$t_2=^{12}C_{2-1}(2r)^{12-2+1}(-3s)^{2-1}\\\\t_2=^{12}C_1 (2r)^{11}(-3s)^{1}\\\\t_2=\frac{12!}{1!11!}(2)^{11}r^{11}(-3)s\\\\t_2=12\cdot (2)^{11}(-3)r^{11}s\\\\t_2=-73728r^{11}s$

Therefore, the second term is -73728r^11 s

A is the correct option.