To factor each expression, we can use the following algebraic techniques:

Difference of squares:

a²-25 = (a+5)(a-5)
c²-8c+16 = (c-4)(c-4)
9x²-16y² = (3x+4y)(3x-4y)

Grouping:

2xy²+4x²y = 2xy(y+2x)
c³-4c = c(c²-4) = c(c-2)(c+2)

Factoring out common factors:

5a²+10ab+5b = 5(a²+2ab+b) = 5(a+b)²

Therefore, the factored forms of the given expressions are:

a²-25 = (a+5)(a-5)c²-8c+16 = (c-4)(c-4) or (c-4)²9x²-16y² = (3x+4y)(3x-4y)2xy²+4x²y = 2xy(y+2x)c³-4c = c(c-2)(c+2)5a²+10ab+5b = 5(a+b)²