# Constant term problem

• Apr 1st 2010, 12:18 PM
Solaris123
Constant term problem
If you are given equation (2x^4+(1/x^3))^7, how do you find the constant term without having to expand it all? You dont have a calculator and you only have 10 minutes.
• Apr 1st 2010, 12:37 PM
Plato
Quote:

Originally Posted by Solaris123
If you are given equation (2x^4+(1/x^3))^7, how do you find the constant term without having to expand it all? You dont have a calculator and you only have 10 minutes.

Each term in the expansion looks like: $\binom{7}{k}\left(2x^4\right)^k\left(x^{-3}\right)^{7-k}$.
Find the value of $k$ which gives $x^0$.
• Apr 1st 2010, 12:48 PM
Solaris123
I must say I don't understand, I mean, there are two values which you can use to make it be x^0 individually but do I have to combine both x in order to then solve for k? and what does that 7 over the k mean?
Edit: more accurately, what did you do and where can I learn how to do it and understand it?
• Apr 1st 2010, 01:15 PM
Plato
Quote:

Originally Posted by Solaris123
I must say I don't understand, I mean, there are two values which you can use to make it be x^0 individually but do I have to combine both x in order to then solve for k? and what does that 7 over the k mean?
Edit: more accurately, what did you do and where can I learn how to do it and understand it?

I don’t know how to answer that question.
Either you know binominal expansion or you don’r.
If you don’t then there is no point in your being asked to do this question.
If you do, then you must know how to do basic algebra.
$\binom{7}{k}\left(2x^4\right)^k\left(x^{-3}\right)^{7-k}=\frac{7!}{k!(7-k)!}2^k\left(x^{7k-21}\right)$.
• Apr 1st 2010, 01:16 PM
Solaris123
So I need to learn Binomial expansion, thank you very much.