Factor. 25m^100-121n^16

(5 m10 - 11 n4) (5 m10 + 11 n4) (5 m50 - 11 n8) 2 (5 m50 - 11 n8) (5 m50 + 11 n8) (5 m10 - 11 n4) 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)