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jcherry99
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)

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