(x + 1) * 6 = x * 6 + ax * 5 + BX * 4 + CX * 3 + DX * 2 + ex + 1, then a + B + C + D + e =?

(x + 1) * 6 = x * 6 + ax * 5 + BX * 4 + CX * 3 + DX * 2 + ex + 1, then a + B + C + D + e =?

According to the binomial coefficient theorem, the coefficients of the sixth power are 1, 6, 15, 20, 15, 6 and 1
So 6 + 15 + 20 + 15 + 6 = 62
Also, when x = 1, (1 + 1) ^ 6 = 64 = 1 + A + B + C + D + e + 1
a+b+c+d+e=64-2=62

Known ax ^ 4 + BX ^ 3 + CX ^ 2 + DX + e = (x-3) ^ 4
Evaluation 1. A + B + C + D + e
2.b+d

ax^4+bx^3+cx^2+dx+e=(x-3)^4
1. Let x = 1, left formula = a + B + C + D + e, right formula = (1-3) ^ 4 = 16;
Left = right, a + B + C + D + e = 16
2. Let x = - 1, left = A-B + C-D + e, right = (- 1-3) ^ 4 = 256;
Left = right, A-B + C-D + e = 256
a+b+c+d+e=16 ①
a-b+c-d+e=256 ②
① - 2 subtracting: 2B + 2D = - 240
So: B + D = - 120