Q=write the sum of the coffeicients in the expansion of (1-3x+ x2 )111 Ans=(-1) Q2=If a and b denote - Maths - Binomial Theorem

Question

Q=write the sum of the coffeicients in the expansion
of (1-3x+ x2 )111 Ans=(-1)
Q2=If a and b denote the sum of coefficients in the
expansions of (1-3x-+10x2 )n and
(1+x)2 respectively ,then write the relation b/w a and b
Ans= a=b3

Ankush Jain · Accepted Answer

1)
Given, expansion = (1-3x +
x2)111 (1)
= (1 + (x2 - 3x))111
Now, in order to find out the sum of the coefficients, we had an
hit and trial method i e , to put the value of x = 1 in (1)
â‡’ sum of coefficients = (1-3(1) +
(1)2)111 = (-1)111 = -1
2)
Given expansions are, (1 - 3x + 10x2
)n and (1 + x2)n
Now, the sum of coefficient of the expansion (1 - 3x +
10x2 )n = a = (1 - 3(1) + 10(1)2
)n
â‡’ a = 8n = 23n (1)
Similarly, sum of coefficients of the expansions (1 +
x2)n = b = (1 + (1)2)n
= 2n
â‡’ b = 2n (2)
On comparing (1) and (2), we get
a = b3

Q=write the sum of the coffeicients in the expansion of (1-3x+ x2 )111 .Ans=(-1) Q2=If a and b denote the sum of coefficients in the expansions of (1-3x-+10x2 )n and (1+x)2 respectively ,then write the relation b/w a and b.Ans= a=b3 .

Q=write the sum of the coffeicients in the expansion of (1-3x+ x² )¹¹¹ .Ans=(-1)

Q2=If a and b denote the sum of coefficients in the expansions of (1-3x-+10x² )ⁿ and (1+x)² respectively ,then write the relation b/w a and b.Ans= a=b³ .