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.

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- Apr 1st 2010, 12:18 PMSolaris123Constant 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 PMPlato
- Apr 1st 2010, 12:48 PMSolaris123
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 PMPlato
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.

$\displaystyle \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 PMSolaris123
So I need to learn Binomial expansion, thank you very much.