Coefficient-of-x-4-in-2-x-3x-2-6-

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 \dots .

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 \dots

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 \dots

[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 \dots