Home
Class 11
MATHS
Show that the coefficient of x^(4) in th...

Show that the coefficient of `x^(4)` in the expansion of `(1+2x+x^(2))^(5) " is " 212`.

Text Solution

Verified by Experts

`(1+2x+x^(2))^(5) = {(1+x)^(2)}^(5) = (1+x)^(10).`
`T_(r+1) = .^(10) C _(r)x^(r). " Coefficent of " x^(4) = .^(10) C _(4) = (( 10 xx 9 xx 8 xx 7 )/(4 xx 3 xx 2 xx 1 ))= 210.`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RS AGGARWAL|Exercise EXERCISE 10A|48 Videos

  • ARITHMETIC PROGRESSION

    RS AGGARWAL|Exercise Exercise 11F (Very Short-Answer Type Questions)|17 Videos

  • CIRCLE

    RS AGGARWAL|Exercise EXERCISE 21 B|18 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^(4) in the expansion of (1-x-2x^(2))^(8) is

The coefficient of x^(3) in the expansion of (1-x+x^(2))^(5) is

The coefficient of x^(4) in the expansion of (1+x+x^(2))^(6) is

The coefficient of x^(4) in the expansion of (1-x)^(-2) is

The coefficient of x^(4) in the expansion of (1+x-2x^(2))^(7) is :

The coefficient of x^(4) in the expansion of (1-ax-x^(2))/(e^(x)) is

The coefficient of x^(r) in the expansion of (1-x)^(-2) is

Find the coefficients of x^4 in the expansion of (1+x+x^2)^3