# Determine the constant term in.

• October 28th 2012, 04:45 AM
Petrus
Determine the constant term in.
Determine the constant term in.https://webwork.math.su.se/webwork2_...1d3f2168b1.png
idk how to solve it :(
• October 28th 2012, 06:37 AM
skeeter
Re: Determine the constant term in.
each term in a binomial expansion is of the form ...

$\binom{n}{k} a^{n-k} b^k$

In this case, $n = 21$ ... the value of $k$ will be such that the variable factors cancel.

$\binom{21}{18} (3x^6)^3\left(\frac{5}{x}\right)^{18}$
• October 28th 2012, 07:05 AM
Petrus
Re: Determine the constant term in.
i did not get it, i dont think i really understand what they want me to answer, with other words i maybe dont understand problem... im confused
• October 28th 2012, 07:59 AM
skeeter
Re: Determine the constant term in.
Quote:

Originally Posted by Petrus
i did not get it, i dont think i really understand what they want me to answer, with other words i maybe dont understand problem... im confused

1. have you learned the binomial theorem?

2. do you understand that a constant term has no variable factors?
• October 28th 2012, 08:05 AM
Petrus
Re: Determine the constant term in.
Quote:

Originally Posted by skeeter
1. have you learned the binomial theorem?

2. do you understand that a constant term has no variable factors?

hi!:)
We have not come here yet, but I want to study in advance. I did read but did not understand clearly i dont like my book :(
• October 28th 2012, 08:18 AM
skeeter
Re: Determine the constant term in.
Quote:

Originally Posted by Petrus
We have not come here yet, but I want to study in advance. I did read but did not understand clearly i dont like my book

your book is not the sole source of knowledge. seek and ye shall find ...

Binomial Theorem (part 1) | Precalculus | Khan Academy
• October 28th 2012, 08:57 AM
Petrus
Re: Determine the constant term in.
ok i did watch and i kinda understand but idk how in my problem to get out the constant term :S
• October 28th 2012, 01:04 PM
skeeter
Re: Determine the constant term in.
I showed you how in post #2.
• October 30th 2012, 10:17 PM
Salahuddin559
Re: Determine the constant term in.
A constant terms comes out when a^n-k * b^k is a constant, and does not involve any variables. In your case, the binomial expansion has only one variable, x. That means, in (3x^6)^n - k * (5/x)^k does not contain any x. For it to happen, when n = 21, you need to equate the power of x to zero, since x^0 = 1, is a constant, and other powers yield terms with x, and so, not a constant term.

(x^6)^21 - k * (1/x)^k = x^0
(x^6)^21 - k * (x^-1)^k = x^0
(x^6)^21 - k * x^-k = x^0
x^(6(21-k) - k) = x^0

Equating coefficients, you get k = 18, which is what he used to get the constant term above.

Salahuddin
Maths online
• October 31st 2012, 04:14 AM
Petrus
Re: Determine the constant term in.
I solved this problem :) forgot to say it ty anyway :)