Find the coefficient of x^{6} y^{3} in the ex | vedclass

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(A) The general term in the expansion of $(x+2y)^{9}$ is given by $T_{r+1} = {}^{9}C_{r} x^{9-r} (2y)^{r}$.This simplifies to $T_{r+1} = {}^{9}C_{r} 2

Vedclass · Accepted Answer

$672$

Vedclass · Answer

(A) The general term in the expansion of $(x+2y)^{9}$ is given by $T_{r+1} = {}^{9}C_{r} x^{9-r} (2y)^{r}$.This simplifies to $T_{r+1} = {}^{9}C_{r} 2^{r} x^{9-r} y^{r}$.To find the coefficient of $x^{6} y^{3}$,we compare the powers of $y$ (or $x$) with $x^{6} y^{3}$,which gives $r = 3$.Substituting $r = 3$ into the expression for the coefficient,we get:Coefficient $= {}^{9}C_{3} 	imes 2^{3} = \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} 	imes 8 = 84 	imes 8 = 672$.

Find the coefficient of $x^{6} y^{3}$ in the expansion of $(x+2 y)^{9}$.

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