From the binomial:
[tex]3x^2y^2-6xy^2[/tex]We can factor out the GCF by factoring out the GCF of the coefficients, and the lowest power of each variable.
The GCF of 3 and 6 is 3.
The lowest power of x is 1.
The lowest power of y is 2.
Then, we can factor out:
[tex]3xy^2[/tex]Multiply each term by:
[tex]\frac{3xy^2}{3xy^2}[/tex]Which does not change the meaning of the expression, since that fraction is equal to 1:
[tex]\begin{gathered} 3x^2y^2-6xy^2=3x^2y^2\times^{}\frac{3xy^2}{3xy^2}-6xy^2\times^{}\frac{3xy^2}{3xy^2} \\ =3xy^2(\frac{3x^2y^2^{}}{3xy^2}-\frac{6xy^2}{3xy^2}) \\ =3xy^2(x-2) \end{gathered}[/tex]Therefore:
[tex]3x^2y^2-6xy^2=3xy^2(x-2)[/tex]