1. Tardigrade
  2. Question
  3. Mathematics
  4. In the expansion of (1 + 3x + 2x2)6, the coefficient of x11 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. In the expansion of $(1 + 3x + 2x^2)^6$, the coefficient of $x^{11}$ is

Binomial Theorem

Solution:

$(1 + 3x + 2x^2)^6 = ((1 +3x) + (2x^2))^6$
$= \,{}^6C_0(1+3x)^6 + \,{}^6C_1(1 + 3x)^5 2x^2 + \,{}^6C_2(1 + 3x)^4(2x^2)^2$
$+ \,{}^6C_3(1 + 3x)^3(2x^2)^3 + \,{}^6C_4(1 + 3x)^2(2x^2)^4 +\,{}^6C_5(1 + 3x) \times$
$(2x^2)^5 + \,{}^6C_6(2x^2)^6$
$\therefore $ Coefficient of $x^{11}$ in above expression
$= \,{}^6C_5\cdot 3\cdot 32$
$ = 6 \times 3 \times 32 = 576$