In the expansion of (1 + 2x-x ^ 2) ^ 4, find the coefficient of x ^ 7?

In the expansion of (1 + 2x-x ^ 2) ^ 4, find the coefficient of x ^ 7?

（1+2x-x2)^4=(x^2-2x-1)^4
The coefficient of x ^ 7 is:
(3C4)*(-2)=-4*2= -8

The coefficient of quadratic expansion of (2x-3) ^ 7 with x ^ 4 term?

The k-th term in (a + b) ^ n is
C(n)(k-1)*a^(n-k+1)*b^(k-1)
Here a = 2x, B = - 3
n=7
Including x ^ 4 items
Then n-k + 1 = 4
k=7+1-4=4
So the fourth term is C (7) 4 * (2x) ^ 4 * (- 3) ^ 3
=35*(16x^4)*(-27)
=-15120x^4
Coefficient = - 15120

(the square of 2x-x-3) + (the square of 5-4x + x) is calculated by the separation coefficient method

(2x squared-x-3) + (5-4x + X squared)
=(2x squared-x-3) + (x squared-4x + 5)
= 2 -1 -3
+) 1 -4 5
3 -5 2
=The square of 3x - 5x + 2