Factor. 25m^100−121n^16(5m10−11n4)(5m10+11n 4)(5m50−11n8)2(5m50−11n8)(5m50+11n8 )(5m10−11n4)2

25m¹⁰⁰-121n¹⁶
this question is a difference of squares. the basic equations is when you get 2 square numbers and you have to find their difference ;
x²-y² = (x+ y)(x-y)
you have to then find the product of these factors.
the question given can be rewritten to write the numbers in their square forms 
25m¹⁰⁰ - 5²m⁵⁰ˣ² - square root - 5m⁵⁰
121n¹⁶ - 11²n⁸ˣ² - square root - 11n⁸
we have to then factorise them 
the answer for 25m¹⁰⁰-121n¹⁶ = (5m⁵⁰ - 11n⁸)  (5m⁵⁰ + 11n⁸)

This is too long-standing now get out