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.
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.
$\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) $.