Binomial Theorem

If A denotes the sum of all the coefficients in the expansion of (1-3x+10x2 )n and B denotes the sum of all the coefficients in the expansion of (1+x2 )n, then :

1. B=A3
2. 3A=B
3. A=3B
4. A=B3

Answer

(4) A=B3

Solution

∵ sum of all coefficients = value of the expression at x=1

A=(1-3+10)n=8n

B=(1+1)n=2n

⇒ A=(23)n=(2n)3=B3

Answer: (4)