InterviewSolution
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InterviewSolution
| 1. |
Find the coefficent of`x^(6)y^(3)` in the expansion of `(x+2y)^(9)`. |
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Answer» The general term in the expansion of `(x+2y)^(9)` is given by `T_(r+1)=.^(9)C_(r) xx x^((9-r)) xx(2y)^(r)` `rArr T_(r+1)=.^(9)C_(r) xx2^(r) xxx^((9-r)) xxy^(r)." "`...(i) We have to find the coeffcient of `x^(6)y^(3)`. Putting r=3 in (i), we get `T_(3+1)=.^(9)C_(3) xx 2^(3) xx (x^(6)y^(3))`. `:." coefficient of "x^(6) y^(3)` in the given expansion `=(.^(9)C_(3) xx 2^(3))=((9 xx8xx7)/(3xx2xx1) xx8) =672`. Hence, the coefficient of `x^(6)y^(3)` in the given expansion is 672. |
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