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Find the containing x^(3) in the expansi...

Find the containing `x^(3)` in the expansion of `(2y-x^((1)/(2)))^(10)`

Text Solution

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Let `x^(3)` occur in the general term `T_(r+1)`
Now, `T_(r+1)+.^(10)C_(r)(2y)^(10-r)(-x^((1)/(2)))^(r)`
Since `x^(3)` occurs in `T_(r+1)`
`thereforex^(3)=x^((r)/(2))implies(r)/(2)=3impliesr=6`
`thereforeT_(6+1)(-1)^(6).^(10)C_(6)(2y)^(4)(x)^(3)`
`=(10xx9xx8xx7)/(4xx3xx2xx1)xx2xx2xx2xx2xxy^(4).x^(3)`
`=3360y^(4)x^(3)`.
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