`(2x^(3)-(1)/(3x^(3)))^(10)` के प्रसार में `x^(6)` का गुणांक ज्ञात कीजिए।

Explanation

माना `(2x^(3)-(1)/(3x^(3)))^(10)` के प्रसार में `(r+1)` वाँ पद `T_(r+1)` है।
`T_(r+1)=.^(10)C_(r)(2x^(3))^(10-r)(-(1)/(3x^(3)))^(r)`
`=.^(10)C_(r)*2^(10-r)*x^(30-3r)*((-1)^(r))/(3^(r)*x^(3r))`
`=.^(10)C_(r)*(2^(10-r)*(-1)^(r))/(3^(r))*x^(30-6r)`
माना `30-6r=6`
`rArr30-6r=24`
`rArrr=4`
`thereforex^(6)` का गुणांक `=.^(10)C_(4)*(2^(10-4)(-1)^(4))/(3^(4))=(lfloor10)/(lfloor6lfloor4)xx(64)/(81)`
`=(7xx8xx9xx10)/(24)xx(64)/(81)=(4480)/(27)`