Coefficient of x^4 in (2−x+3x^2 )^6 =?


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Question Number 48443 by rahul 19 last updated on 24/Nov/18

$C o e f f i c i e n t o f x^{4} i n {(2 - x + 3 x^{2})}^{6} = ?$
Commented by rahul 19 last updated on 24/Nov/18

$D o b y m u l t i n o m i a l e x p a n s i o n s . . . .$
Commented by Meritguide1234 last updated on 24/Nov/18

$r a h u l y o u r p o s t a r e n i c e p o s t m o r e q u e s t i o n s l i k e t h i s$
Commented by rahul 19 last updated on 24/Nov/18

$S u r e s i r!$ $I^{'} l l p o s t t o m o r r o w . . .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 24/Nov/18

	$\frac{6!}{a! b! c!} {(2)}^{a} {(- x)}^{b} {(3 x^{2})}^{c}$ $= \frac{6!}{a! b! c!} {(2)}^{a} {(3)}^{c} {(- 1)}^{b} {(x)}^{b + 2 c}$ $a + b + c = 6$ $b + 2 c = 4$ $b = 0 c = 2 s o a = 4$ $b = 2 c = 1 a = 3$ $b = 4 c = 0 a = 2$ $s o r e q u i r e d c o e f f i c i e n t i s$ $[\frac{6!}{4! 0! 2!} \times {(2)}^{4} {(3)}^{2} {(- 1)}^{0} + \frac{6!}{3! 2! 1!} \times {(2)}^{3} {(3)}^{1} {(- 1)}^{2} +$ $\frac{6!}{2! 4! 0!} \times {(2)}^{2} {(3)}^{0} {(- 1)}^{4}]$ $p l s c h e c k a n d c a l c u l a t e . . .$ $[15 \times 16 \times 9 + 60 \times 8 \times 3 + 15 \times 4$ $= 2160 + 1440 + 60$ $= 3660$
	Commented by rahul 19 last updated on 24/Nov/18
	=3660. (2160+1440+60)...I forgot the last case! thanks sir ��
	Commented by tanmay.chaudhury50@gmail.com last updated on 24/Nov/18

	$t h a n k y o u f o r r e c h e c k i n c a l c u l a t i o n$ $i h a v e u s e d 3! t w i c e b y m i s t a k e . . .$
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