Question

Find 5 th term in the binomial expansion of (2x-7)^4​

Answer 1

The fifth term in the binomial expansion of $(2x-7)^4$ is 2401

The expansion of a binomial's powers is described by the binomial theorem, a mathematical statement. The polynomial $(x+y)^n$ can be expanded into a sequence of sums made up of terms of the type $cx^ay^b;a,b\in W$ or we can say that a,b are non-negative integers and c is any integer.

The general term of a binomial expansion of (a+b)^n is given by :

$T_{r+1}=^nC_ra^{n-r}b^r$

The given binomial expansion is  $(2x-7)^4$ . Comparing the above expansion to this we get :

$a=2x , b =-7$

Now we have to find the 5th term of the expansion.

$\therefore r+1=5\\or, r = 4$

Using these values in the above formula for the general terms we get:

$T_{5}= {}^4C_4\cdot(2x)^{4-4}\cdot(-7)^4\\or, T_{5}={}^4C_4\cdot(2x)^{0}\cdot(-7)^4\\or,T_5=1\cdot(1)\cdot(2401)\\or,T_5=2401$

Therefore the 5th term in the binomial expansion of $(2x-7)^4$ is 2401.

Learn more about binomial expansion at:

https://brainly.in/question/54103632

https://brainly.in/question/54180503

#SPJ1