What is the greatest common factor of: 16 m 2 n 2 − 12 m n 2 + 20 m 2 n ?

The GCF is 4mn.

Step-by-step explanation:

16 m^2*n^2 − 12 m*n^2 + 20 m^2*n is the correct way to write this expression.

Note that there are 3 terms, and that 4 is common to all three coefficients.  Therefore,

16 m^2*n^2 − 12 m*n^2 + 20 m^2*n  =  4(4 m^2*n^2 − 3 m*n^2 + 5 m^2*n).

Also note that m and n are common to all three terms, but only in the first power:  m^1 and n^1.

Thus, 4(4 m^2*n^2 − 3 m*n^2 + 5 m^2*n)  =  (4mn)(m*n - 3n + 5 m)

The GCF is 4mn.

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