completely factor this expression?
6m^2n - 12mn^2 - 10mn + 20n^2
\(\begin{array}{|rcll|} \hline && 6m^2n - 12mn^2 - 10mn + 20n^2 \\ &=& 2n ( 3m^2 - 6mn - 5m + 10n) \\ &=& 2n (m-2n) (3m-5) \\ \hline \end{array}\)
Factor the following:
6 m^2 n - 12 m n^2 - 10 m n + 20 n^2
Factor 2 n out of 6 m^2 n - 12 m n^2 - 10 m n + 20 n^2:
2 n (3 m^2 - 6 m n - 5 m + 10 n)
Factor terms by grouping. 3 m^2 - 6 m n - 5 m + 10 n = (10 n - 6 m n) + (3 m^2 - 5 m) = m (3 m - 5) - 2 n (3 m - 5):
2 n m (3 m - 5) - 2 n (3 m - 5)
Factor 3 m - 5 from m (3 m - 5) - 2 n (3 m - 5):
Answer: | 2n (3m - 5) (m - 2n)