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

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

Calcular

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

Pasos da solución

Combina \frac{3}{5}wz e \frac{2}{3}zw para obter \frac{19}{15}wz.

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

Combina -\frac{1}{8}z^{2} e \frac{5}{9}z^{2} para obter \frac{31}{72}z^{2}.

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

Combina \frac{19}{15}wz e -\frac{wz}{9} para obter \frac{52}{45}wz.

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

Combina \frac{31}{72}z^{2} e -\frac{z^{2}}{72} para obter \frac{5}{12}z^{2}.

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

Factorizar

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

Pasos da solución

Factoriza \frac{1}{360}.

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

Considera 216wz-45z^{2}+240zw+200z^{2}-40wz-5z^{2}. Factoriza z.

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

Considera 216w-45z+240w+200z-40w-5z. Multiplica e combina termos semellantes.

$$150z+416w$$

Considera 150z+416w. Factoriza 2.

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

Reescribe a expresión factorizada completa.

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