Solve 4/9mn+11/18m^2+5/12n^2+7/6m^2+frac{4}{3}mn-frac{9}{4}n^2

$$\frac { 4 } { 9 } m n + \frac { 11 } { 18 } m ^ { 2 } + \frac { 5 } { 12 } n ^ { 2 } + \frac { 7 } { 6 } m ^ { 2 } + \frac { 4 } { 3 } m n - \frac { 9 } { 4 } n ^ { 2 }$$

Evaluate

$$\frac{16mn}{9}+\frac{16m^{2}}{9}-\frac{11n^{2}}{6}$$

Solution Steps

Combine \frac{11}{18}m^{2} and \frac{7}{6}m^{2} to get \frac{16}{9}m^{2}.

$$\frac{4}{9}mn+\frac{16}{9}m^{2}+\frac{5}{12}n^{2}+\frac{4}{3}mn-\frac{9}{4}n^{2}$$

Combine \frac{4}{9}mn and \frac{4}{3}mn to get \frac{16}{9}mn.

$$\frac{16}{9}mn+\frac{16}{9}m^{2}+\frac{5}{12}n^{2}-\frac{9}{4}n^{2}$$

Combine \frac{5}{12}n^{2} and -\frac{9}{4}n^{2} to get -\frac{11}{6}n^{2}.

$$\frac{16}{9}mn+\frac{16}{9}m^{2}-\frac{11}{6}n^{2}$$

Factor

$$\frac{32m^{2}+32mn-33n^{2}}{18}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{16mn+22m^{2}+15n^{2}+42m^{2}+48mn-81n^{2}}{36}$$

Consider 16mn+22m^{2}+15n^{2}+42m^{2}+48mn-81n^{2}. Multiply and combine like terms.

$$64m^{2}+64mn-66n^{2}$$

Consider 64m^{2}+64mn-66n^{2}. Factor out 2.

$$2\left(32m^{2}+32mn-33n^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{32m^{2}+32mn-33n^{2}}{18}$$