Factor. 25m^100 - 121n^16

This is a difference of squares. Difference of squares factor like this.

a^2 - b^2 = (a + b) (a - b)

In your question all 4 factors must be perfect squares in order to use this property.

25 = 5*5

m^100 = m^50 * m^50

121 = 11 * 11

n^16 = n^8 * n*8

All four parts are perfect squares as required.

a = 5m^50

b = 11n^8

a^2 - b^2 = (5m^50 - 11n^8) (5m^50 + 11n^8)