Resolver 3/2x^5y^3-27/8x^3y^5

$$\frac { 3 } { 2 } x ^ { 5 } y ^ { 3 } - \frac { 27 } { 8 } x ^ { 3 } y ^ { 5 }$$

Factorizar

$$\frac{3\left(2x-3y\right)\left(2x+3y\right)x^{3}y^{3}}{8}$$

Pasos da solución

Factoriza \frac{3}{8}.

$$\frac{3\left(4x^{5}y^{3}-9x^{3}y^{5}\right)}{8}$$

Considera 4x^{5}y^{3}-9x^{3}y^{5}. Factoriza x^{3}y^{3}.

$$x^{3}y^{3}\left(4x^{2}-9y^{2}\right)$$

Considera 4x^{2}-9y^{2}. Reescribe 4x^{2}-9y^{2} como \left(2x\right)^{2}-\left(3y\right)^{2}. Pódese factorizar a diferenza dos cadrados usando a regra: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-3y\right)\left(2x+3y\right)$$

Reescribe a expresión factorizada completa.

$$\frac{3x^{3}y^{3}\left(2x-3y\right)\left(2x+3y\right)}{8}$$

Calcular

$$\frac{3\left(4x^{2}-9y^{2}\right)\left(xy\right)^{3}}{8}$$