First slide

Binomial theorem for positive integral Index

Question

$T h e c o e f f i c i e n t o f t h e m i d d l e t e r m i n t h e b i n o m i a l e x p a n s i o n i n p o w e r s o f x o f {(1 + a x)}^{4} a n d o f {(1 - a x)}^{6} i s t h e s a m e i f a =$

Easy

A

$\frac{3}{5}$
B

$\frac{10}{3}$
C

$\frac{3}{10}$
D

$- \frac{3}{10}$

Solution

$M i d d l e t e r m i n t h e e x p a n s i o n o f {(1 + a x)}^{4} i s C (4, 2) {(a x)}^{2} a n d M i d d l e t e r m i n t h e e x p a n s i o n o f {(1 - a x)}^{6} i s C (6, 3) {(- a x)}^{3} E q u a t e t h e s e t w o c o f f i c i e i n t s o f t e r m s C (4, 2) a^{2} = - C (6, 3) a^{3} 6 = - 20 a a = - \frac{3}{10}$

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