To prove that `25m^2-40mn +16n^2` is non-negative for all values of m and n, set the polynomial greater than and equal to zero.
Then, consider this property of exponent which is:
`x^ngt=0 ` when n is an even number.
Since the exponent of the factor `5m-4n` is 2 which is an evennumber, then the inequality equation `(5m - 4n)^2gt=0` is always true.
Hence, `25m^2-40mn +16n^2` is non-negative for any values of m and n.