In the expansion of X (1-x) ^ 4 + x ^ 2 (1 + 2x) ^ 8 + x ^ 3 (1 + 3x) ^ 12, the coefficient of x ^ 4 is

In the expansion of X (1-x) ^ 4 + x ^ 2 (1 + 2x) ^ 8 + x ^ 3 (1 + 3x) ^ 12, the coefficient of x ^ 4 is

In X (1-x) ^ 4, the cubic term of the expansion of (1-x) ^ 4
C(4,3)(-x)^3
The coefficient is C (4,3) (- 1) ^ 3 = - 4
In x ^ 2 (1 + 2x) ^ 8, the quadratic term of X in the expansion of (1 + 2x) ^ 8
C(8,6)(2x)^2
The coefficient is C (8,6) (2) ^ 2 = 112
In x ^ 3 (1 + 3x) ^ 12, the first power term of X in the expansion of (1 + 3x) ^ 12
C(12,11)(3x)^1
The coefficient is C (12,11) (3) ^ 1 = 36,
So the coefficient of x ^ 4 is - 4 + 112 + 36 = 144

If the power of 3x is 2, the power of Y is n and the power of - 2x is m, then M = () n = ()

Is it the same kind?
X and y are equal in degree respectively
So m = 2
n=1

If a (x ^ m times the fourth power of Y) ^ 3 ÷ (3x ^ 2 times y ^ n) ^ 2 = 2x ^ 5 times y ^ 4, then a =? M =? N =?

That is, coefficient = A / 9 = 2
a=18
X times = 3m-4 = 5
m=3
Y times 12-2n = 4
n=4