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# completely factor this expression?

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6m^2n - 12mn^2 - 10mn + 20n^2

Guest Jul 20, 2017
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#1
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completely factor this expression?

6m^2n - 12mn^2 - 10mn + 20n^2

$$\begin{array}{|rcll|} \hline && 6m^2n - 12mn^2 - 10mn + 20n^2 \\ &=& 2n ( 3m^2 - 6mn - 5m + 10n) \\ &=& 2n (m-2n) (3m-5) \\ \hline \end{array}$$

heureka  Jul 20, 2017
#2
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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)

Guest Jul 20, 2017

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