Solve 3/5wz-1/8z^2+2/3zw+5/9z^2-frac{wz}{9}-frac{z^2}{72}

$$\frac { 3 } { 5 } w z - \frac { 1 } { 8 } z ^ { 2 } + \frac { 2 } { 3 } z w + \frac { 5 } { 9 } z ^ { 2 } - \frac { w z } { 9 } - \frac { z ^ { 2 } } { 72 }$$

Evaluate

$$\frac{52wz}{45}+\frac{5z^{2}}{12}$$

Solution Steps

Combine \frac{3}{5}wz and \frac{2}{3}zw to get \frac{19}{15}wz.

$$\frac{19}{15}wz-\frac{1}{8}z^{2}+\frac{5}{9}z^{2}-\frac{wz}{9}-\frac{z^{2}}{72}$$

Combine -\frac{1}{8}z^{2} and \frac{5}{9}z^{2} to get \frac{31}{72}z^{2}.

$$\frac{19}{15}wz+\frac{31}{72}z^{2}-\frac{wz}{9}-\frac{z^{2}}{72}$$

Combine \frac{19}{15}wz and -\frac{wz}{9} to get \frac{52}{45}wz.

$$\frac{52}{45}wz+\frac{31}{72}z^{2}-\frac{z^{2}}{72}$$

Combine \frac{31}{72}z^{2} and -\frac{z^{2}}{72} to get \frac{5}{12}z^{2}.

$$\frac{52}{45}wz+\frac{5}{12}z^{2}$$

Factor

$$\frac{z\left(75z+208w\right)}{180}$$

Solution Steps

Factor out \frac{1}{360}.

$$\frac{216wz-45z^{2}+240zw+200z^{2}-40wz-5z^{2}}{360}$$

Consider 216wz-45z^{2}+240zw+200z^{2}-40wz-5z^{2}. Factor out z.

$$z\left(216w-45z+240w+200z-40w-5z\right)$$

Consider 216w-45z+240w+200z-40w-5z. Multiply and combine like terms.

$$150z+416w$$

Consider 150z+416w. Factor out 2.

$$2\left(75z+208w\right)$$

Rewrite the complete factored expression.

$$\frac{z\left(75z+208w\right)}{180}$$