If A denotes the sum of all the coefficients in the expansion of 1 - 3 x + 10 x 2 n and B denotes the sum of all the coefficients in the expansion of 1 + x 2 n , then :

Step-by-step solution

We have, A = Sum of the coefficients in the expansion of ⇒ 1 - 3 x + 10 x 2 n = ( 1 - 3 + 10 ) n = ( 8 ) n = ( 2 ) 3 n (putting x = 1 ) Now, B = Sum of the coefficients in the expansion of ⇒ 1 + x 2 n = ( 1 + 1 ) n = 2 n Clearly, A = B 3 .