Question

Factor: 25m^8 - 60m^4n + 36n^2

Answer 1

25m^8 - 60m^4n + 36n^2
This can be rewritten as
(5m^4)^2 - 2(5m^4)(6n) + (6n)^2
This is of the form a^2 - 2ab + b^2 and hence using identity
a^2 - 2ab + b^2 = (a - b)^2
(5m^4)^2 - 2(5m^4)(6n) + (6n)^2 = (5m^4 - 6n)^2

so 25m^8 - 60m^4n + 36n^2 = (5m^4 - 6n)^2