Final answer:
To find the coefficient of x^25y^16 in the expansion of (-4x^5 + 4y^2)^13, use the binomial theorem and the formula for the coefficient of x^a*y^b in the expansion of (x + y)^n.
Step-by-step explanation:
To find the coefficient of x25y16 in the expansion of (-4x5 + 4y2)13, we can use the binomial theorem.
The formula for the coefficient of xayb in the expansion of (x + y)n is given by:
C(n, b) * an-b * bb,
where C(n, b) represents the combination of n items taken b at a time.
In this case, n = 13, a = 5, and b = 2. Plugging these values into the formula:
C(13, 2) * 513-2 * 22 = (13! / (2! * (13-2)!)) * 511 * 22
Simplifying this expression will give us the coefficient of x25y16 in the expansion of (-4x5 + 4y2)13.