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6\left(15au-6av-25yu+10yv\right)
Factor out 6.
3a\left(5u-2v\right)-5y\left(5u-2v\right)
Consider 15au-6av-25yu+10yv. Do the grouping 15au-6av-25yu+10yv=\left(15au-6av\right)+\left(-25yu+10yv\right), and factor out 3a in the first and -5y in the second group.
\left(5u-2v\right)\left(3a-5y\right)
Factor out common term 5u-2v by using distributive property.
6\left(5u-2v\right)\left(-5y+3a\right)
Rewrite the complete factored expression.