Solve 3/5m^2-2mn+1/10m^2-1/3nm+2nm-2m^2

$$\frac { 3 } { 5 } m ^ { 2 } - 2 m n + \frac { 1 } { 10 } m ^ { 2 } - \frac { 1 } { 3 } n m + 2 n m - 2 m ^ { 2 }$$

Evaluate

$$-\frac{mn}{3}-\frac{13m^{2}}{10}$$

Solution Steps

Combine \frac{3}{5}m^{2} and \frac{1}{10}m^{2} to get \frac{7}{10}m^{2}.

$$\frac{7}{10}m^{2}-2mn-\frac{1}{3}nm+2nm-2m^{2}$$

Combine -2mn and -\frac{1}{3}nm to get -\frac{7}{3}mn.

$$\frac{7}{10}m^{2}-\frac{7}{3}mn+2nm-2m^{2}$$

Combine -\frac{7}{3}mn and 2nm to get -\frac{1}{3}mn.

$$\frac{7}{10}m^{2}-\frac{1}{3}mn-2m^{2}$$

Combine \frac{7}{10}m^{2} and -2m^{2} to get -\frac{13}{10}m^{2}.

$$-\frac{13}{10}m^{2}-\frac{1}{3}mn$$

Factor

$$\frac{m\left(-39m-10n\right)}{30}$$

Solution Steps

Factor out \frac{1}{30}.

$$\frac{18m^{2}-60mn+3m^{2}-10nm+60nm-60m^{2}}{30}$$

Consider 18m^{2}-60mn+3m^{2}-10nm+60nm-60m^{2}. Factor out m.

$$m\left(18m-60n+3m-10n+60n-60m\right)$$

Consider 18m-60n+3m-10n+60n-60m. Multiply and combine like terms.

$$-39m-10n$$

Rewrite the complete factored expression.

$$\frac{m\left(-39m-10n\right)}{30}$$