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Find the coefficient of x^{3} in the given expansion of (1+2x)^5

 

Option: 1

20


Option: 2

10


Option: 3

5


Option: 4

5


Answers (1)

best_answer

Given

(1+2x)^5

Where a=1,b=2x  , and n=5

Let the term x^3 occurs in the (r+1)^{th} term then 

\begin{gathered} T_{r+1}=5 c_r(1)^{5-r}(2 x)^r \\\\ x^3=5 c_r 2^r(1)^{5-r}(x)^r \end{gathered}

By comparing on both sides, r=3 is obtained.


So, coefficient of x^{3} is   5 c_3 2^3(1)^{5-3}

5 c_3 2^3(1)^{5-3}=5 c_3 2^3=\left(\frac{5 !}{3 ! 2 !}\right)=10

Posted by

vishal kumar

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