If ' a ' be the sum of the odd terms ' b ' be the sum of the even terms in the expansion of (1+ x ) n , then (1-x)n is equal to -

Question

If ' a ' be the sum of the odd terms ' b ' be the sum of the even terms in the expansion of (1+ x ) n , then (1-x)n is equal to - (A) a-b (B) a+b (C) b - a (D) none

Tardigrade Admin · Accepted Answer

Given (1+ x ) n = a + b ldots ldots(1) then, (1- x ) n = a - b ldots ldots(2) Multiplying equation (1) (2) we get, (1- x 2) n = a 2- b 2

Q. If ' $a$ ' be the sum of the odd terms & ' $b$ ' be the sum of the even terms in the expansion of $(1 + x)^{n}$ , then $(1 - x)^{n}$ is equal to -

$a - b$

$a + b$

$b - a$

none

Given $(1 + x)^{n} = a + b \dots\dots (1)$
then, $(1 - x)^{n} = a - b \dots\dots (2)$
Multiplying equation (1) & (2)
we get, $(1 - x^{2})^{n} = a^{2} - b^{2}$

Q. If ' a ' be the sum of the odd terms & ' b ' be the sum of the even terms in the expansion of (1+x)n, then (1−x)n is equal to -

a−b

a+b

b−a