Let `n` be a positive integer and `(1+x+x^2)^n=a_0+a_1x++a^(2n)x^(2n)dot` Show that `a_0^2-a_1^ 2+a_2^ 2++'a_2n' x^2=a_ndot`

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x_(2n), find the value of a_0+a_6++ ,n in Ndot

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

Given (1-2x+5x^2-10 x^3)(1+x)^n=1+a_1x+a_2x^2+ and that a1 2=2a_2 then the value of n is.

If (1 +x+x^2)^25 = a_0 + a_1x+ a_2x^2 +..... + a_50.x^50 then a_0 + a_2 + a_4 + ... + a_50 is :

If (18 x^2+12 x+4)^n=a_0+a_(1x)+a2x2++a_(2n)x^(2n), prove that a_r=2^n3^r(^(2n)C_r+^n C_1^(2n-2)C_r+^n C_2^(2n-4)C_r+) .

If (1+2x+3x^2)^(10)=a_0+a_1x+a_2x^2++a_(20)x^(20),t h e na_1 equals 10 b. 20 c. 210 d. none of these

Find the sum of the coefficients in the expansion of (1+2x+3x^2+ n x^n)^2dot

If (1 + ax + b x^2)^4 = a_0 +a_1 x + a_2 x^2 +...+a_8 x^8 when a,b,a_0,a_1,a_2...,a_8 in R such that a_0+a_1+a_2 != 0 and |(a_0,a_1,a_2),(a_1,a_2,a_0),(a_2,a_0,a_1)|=0 then the value of 5a/b (A) 6 (B) 8 (C) 10 (D) 12