Resolver x^6y^6-x^3y^3

$$x ^ { 6 } y ^ { 6 } - x ^ { 3 } y ^ { 3 }$$

Factorizar

$$x^{3}y^{3}\left(xy-1\right)\left(x^{2}y^{2}+xy+1\right)$$

Pasos da solución

Factoriza x^{3}y^{3}.

$$x^{3}y^{3}\left(x^{3}y^{3}-1\right)$$

Considera x^{3}y^{3}-1. Reescribe x^{3}y^{3}-1 como \left(xy\right)^{3}-1^{3}. Pódese factorizar a diferenza dos cubos usando a regra: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(xy-1\right)\left(x^{2}y^{2}+xy+1\right)$$

Reescribe a expresión factorizada completa.

$$x^{3}y^{3}\left(xy-1\right)\left(x^{2}y^{2}+xy+1\right)$$

Calcular

$$\left(xy\right)^{3}\left(\left(xy\right)^{3}-1\right)$$