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u^{2}+4vu-60v^{2}
Consider u^{2}+4uv-60v^{2} as a polynomial over variable u.
\left(u+10v\right)\left(u-6v\right)
Find one factor of the form u^{k}+m, where u^{k} divides the monomial with the highest power u^{2} and m divides the constant factor -60v^{2}. One such factor is u+10v. Factor the polynomial by dividing it by this factor.