In the expansion of (2-x+3x^2)^6 the coefficient o

Question

In the expansion of (2-x+3x^2)^6 the coefficient of x^5 is

Arun Kumar · Accepted Answer

Hello Student,The general term in expansion iss=5-2t$ and $r=1+t \\=>t=0=>r=1,s=5 \\=>t=1=>r=2,s=3 \\=>t=2=>r=3,s=1 \\$three terms$ \\ {6! 2^1(-1)^53^tx^{5} \over 1!5!0!}+{6! 2^2(-1)^33^1x^{3+2} \over 2!3!1!}+{6! 2^3(-1)^13^2x^{1+2*2} \over 3!1!2!} \\=>-12-720-4320=-5052 src=http://latex.codecogs.com/gif.latex?%5C%5C%20%7B6%21%202%5Er%28-x%29%5Es%283x%5E2%29%5Et%20%5Cover%20r%21s%21t%21%7D%20%5C%5C%3D%7B6%21%202%5Er%28-1%29%5Es3%5Etx%5E%7Bs&plus;2t%7D%20%5Cover%20r%21s%21t%21%7D%20%5C%5Cr&plus;s&plus;t%3D6%20%5C%5C%24for%20%24x%5E5%20%5C%5Cs&plus;2t%3D5%20%5C%5C%3D%3Es%3D5-2t%24%20and%20%24r%3D1&plus;t%20%5C%5C%3D%3Et%3D0%3D%3Er%3D1%2Cs%3D5%20%5C%5C%3D%3Et%3D1%3D%3Er%3D2%2Cs%3D3%20%5C%5C%3D%3Et%3D2%3D%3Er%3D3%2Cs%3D1%20%5C%5C%24three%20terms%24%20%5C%5C%20%7B6%21%202%5E1%28-1%29%5E53%5Etx%5E%7B5%7D%20%5Cover%201%215%210%21%7D&plus;%7B6%21%202%5E2%28-1%29%5E33%5E1x%5E%7B3&plus;2%7D%20%5Cover%202%213%211%21%7D&plus;%7B6%21%202%5E3%28-1%29%5E13%5E2x%5E%7B1&plus;2*2%7D%20%5Cover%203%211%212%21%7D%20%5C%5C%3D%3E-12-720-4320%3D-5052>Thanks & RegardsArun KumarBtech, IIT DelhiAskiitians Faculty

Algebra> In the expansion of (2-x+3x^2)^6 the coef...

In the expansion of (2-x+3x^2)^6 the coefficient of x^5 is

MYQUESTIONS , 11 Years ago

Arun Kumar

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Algebra> In the expansion of (2-x+3x^2)^6 the coef...

In the expansion of (2-x+3x^2)^6 the coefficient of x^5 is

MYQUESTIONS , 11 Years ago

Arun Kumar

LIVE ONLINE CLASSES

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