In the expansion of {(1 + 3x + 2{x^2})^6} the | vedclass

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Question

(d) ${(1 + 3x + 2{x^2})^6}$ = ${[1 + x(3 + 2x)]^6}$

= $1 + {\,^6}{C_1}x(3 + 2x){ + ^6}{C_2}{x^2}{(3 + 2x)^2}$${ + ^6}{C_3}{x^3}{(3 + 2x)^3}{ + ^6}{

Vedclass · Accepted Answer

$576$

Vedclass · Answer

(d) ${(1 + 3x + 2{x^2})^6}$ = ${[1 + x(3 + 2x)]^6}$

= $1 + {\,^6}{C_1}x(3 + 2x){ + ^6}{C_2}{x^2}{(3 + 2x)^2}$${ + ^6}{C_3}{x^3}{(3 + 2x)^3}{ + ^6}{C_4}{x^4}{(3 + 2x)^4}$${ + ^6}{C_5}{x^5}{(3 + 2x)^5}{ + ^6}{C_6}{x^6}{(3 + 2x)^6}$

Only ${x^{11}}$ gets from $^6{C_6}{x^6}{(3 + 2x)^6}$

$	herefore $ $^6{C_6}{x^6}{(3 + 2x)^6} = \,{x^6}{(3 + 2x)^6}$

$	herefore $ Coefficient of ${x^{11}}$ = $^6{C_5}{3.2^5} = 576$.

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

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