Grade 12Algebra

the expression

[x+(xpower3-1)power1/2 ]power5+[x-(xpower3-1)power1/2]power5. is a polynomial of degree

plz solve immediately with full steps thank you.

ravi kumar tyagi

15 Years agoGrade 12

2 Answers

SAGAR SINGH - IIT DELHI

15 Years ago

Dear student,

Use binomial theorem....

$\begin{displaymath} (a+b)^n = a^n + n a^{n-1}b + {n(n-1)\over 2} a^{n-2}b^2 + ... + b^n \end{displaymath}$

But what are all those terms in the middle? We write them in terms of combination notation

$\begin{displaymath} \left(\!\!\! \begin{array}{c} n \\ m \end{array} \!\!\!\right) = \frac{n!}{m!(n-m)!} \end{displaymath}$

This means the "combination of n things taken m at a time". This is also sometimes written as ${^n}C_m$ . Then we can write the binomial expansion as
$\begin{displaymath} (a+b)^n = \sum_{m=0}^n \left(\!\!\! \begin{array}{c} n \\ m \end{array} \!\!\!\right) a^m b^{n-m} \end{displaymath}$