Hey! I'm guessing the question that your polynomial came from was about finding a specific term, not the whole polynomial. This is part of the permutations and combinations unit called "binomial expansion"
Since you didn't specify which term, I'm going to give you the general formula and an example. Hopefully, that will be enough information for you to solve the question!
The general formula is that the "rth" term of (a+b)n = nCr * (an-r * br). In this formula, n is the exponent, r is the term we're looking for, a is your first term of the binomial, and b is the second term of the polynomial. That C the math function combination. With your polynomial, this turns into:
10Cr * x10-r * (2y)r
Remember, we begin on the first term is r = 0 we go up to r = 10
Now for a specific example: What is the 6th term of (x+2y)10?
If the first term is r = 0, the 6th term is r = 5
10C5 * x10-5 * (2y)5
252 * x5 * 32y5
The sixth term is: 8064x5y5
I hope that helped! Feel free to reach out if you have any other questions or if you want someone else to answer this question. Everyone learns differently, so if my explanation doesn't make sense, that's okay!
2 years ago
Answered By Emily D
Hey! I'm guessing the question that your polynomial came from was about finding a specific term, not the whole polynomial. This is part of the permutations and combinations unit called "binomial expansion"
Since you didn't specify which term, I'm going to give you the general formula and an example. Hopefully, that will be enough information for you to solve the question!
The general formula is that the "rth" term of (a+b)n = nCr * (an-r * br). In this formula, n is the exponent, r is the term we're looking for, a is your first term of the binomial, and b is the second term of the polynomial. That C the math function combination. With your polynomial, this turns into:
10Cr * x10-r * (2y)r
Remember, we begin on the first term is r = 0 we go up to r = 10
Now for a specific example: What is the 6th term of (x+2y)10?
If the first term is r = 0, the 6th term is r = 5
10C5 * x10-5 * (2y)5
252 * x5 * 32y5
The sixth term is: 8064x5y5
I hope that helped! Feel free to reach out if you have any other questions or if you want someone else to answer this question. Everyone learns differently, so if my explanation doesn't make sense, that's okay!