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ad-work [718]
3 years ago
5

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

Mathematics
2 answers:
Goshia [24]3 years ago
5 0
It is A, my friend. I have taken the test and got it right ;)


ZanzabumX [31]3 years ago
3 0

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.



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