Question

What is the second term in the binomial expansion?

Answer 1

\[(2r-3s)^{12}\]

Answer 2

I had a question like this.
http://openstudy.com/users/languageenthusiast#/updates/52a60355e4b04c50ef975c41

\[(x+y)^n = \sum_{k=0}^n \binom{n}{k}x^{n-k}y^k.\]
Let:
x = 2r
y = -3s
n = 12

Answer 3

I know the formula is in the form (x+y)^n but how do I get that form with (2r-3s)?

Answer 4

\[(2r-3s)^{12} = \sum_{k=0}^{12} \binom{12}{0}x^{12-0}-3s^0.\]
Go from \(k = 0~to~k = 12\).

Answer 5

Oops!
\[(2r-3s)^{12} = \sum_{k=0}^{12} \binom{12}{0}2r^{12-0}-3s^0.\]

Answer 6

what is that E looking thing represent. I remember going over it in class, but forget

Answer 7

It is the Greek capital letter Sigma.
It means to add over a series of numbers (summation).

Answer 8

Khan academy goes over the binomial theorem:
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/binomial_theorem/v/binomial-theorem--part-1

Answer 9

So how do I determine what series of numbers it includes? Like why 12 and k=0?

Answer 10

Remember that your binomial is raised to the power of 12?
\[(2r-3s)^{12} = \sum_{k=0}^{12} \binom{12}{0}2r^{12-0}-3s^0.\]
See how there is a twelve above the capital sigma?
This means to go from k = 0 to k = 12.

Answer 11

Okay thanks! I'll just watch the video! lol

Answer 12

Best of luck!

Answer 13

I may leave somewhere soon, so if you return and want to check your answer the answer is:
\[4096 r^12-73728 r^11 s+608256 r^10 s^2-3041280 r^9 s^3+10264320 r^8 s^4\]\[-24634368 r^7 s^5+43110144 r^6 s^6-55427328 r^5 s^7+51963120 r^4 s^8-34642080 r^3\]\[s^9+15588936 r^2 s^10-4251528 r s^11+531441 s^12\]

You have 13 terms.