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

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

Factor

$$\frac{2mny+24mn+32m^{2}-33n^{2}}{18}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{4ymn+22m^{2}+15n^{2}+42m^{2}+48mn-81n^{2}}{36}$$

Consider 4ymn+22m^{2}+15n^{2}+42m^{2}+48mn-81n^{2}. Multiply and combine like terms.

$$4mny+48mn-66n^{2}+64m^{2}$$

Consider 4mny+48mn-66n^{2}+64m^{2}. Factor out 2.

$$2\left(2mny+24mn-33n^{2}+32m^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{2mny+24mn-33n^{2}+32m^{2}}{18}$$

Evaluate

$$\frac{mny}{9}+\frac{4mn}{3}+\frac{16m^{2}}{9}-\frac{11n^{2}}{6}$$