find coefficient of x^(r ) in the expension of (2x−6y)^(−8)


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Question Number 73628 by Waseem Yaqoob last updated on 14/Nov/19

$f i n d c o e f f i c i e n t o f x^{r} i n t h e e x p e n s i o n o f$ ${(2 x - 6 y)}^{- 8}$
	Answered by mr W last updated on 14/Nov/19

	${(2 x - 6 y)}^{- 8}$ $= {(- 6 y)}^{- 8} {(1 - \frac{x}{3 y})}^{- 8}$ $= {(- 6 y)}^{- 8} \underset{r = 0}{\sum^{\infty}} C_{7}^{r + 7} {(\frac{x}{3 y})}^{r}$ $c o e f . o f x^{r} :$ $a_{r} = {(- 6 y)}^{- 8} {(\frac{1}{3 y})}^{r} C_{7}^{r + 7} = \frac{C_{7}^{r + 7}}{2^{8} {(3 y)}^{8 + r}}$ $e x a m p l e :$ $a_{5} = \frac{C_{7}^{12}}{2^{8} {(3 y)}^{13}} = \frac{11}{5668704 y^{13}}$
	Commented by Waseem Yaqoob last updated on 16/Nov/19

	$K i n d l y c h e k a n d g i v e a n s w e r o f q$ $73723 + 73724 + 73725$
	Commented by Waseem Yaqoob last updated on 16/Nov/19

	Commented by mr W last updated on 16/Nov/19

	$i a n s w e r a q u e s t i o n w h e n i c a n a n d$ $w h e n i l i k e, a u t o m a t i c a l l y .$
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