Solve x^2y^4-x^6

$$x ^ { 2 } y ^ { 4 } - x ^ { 6 }$$

Factor

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

Solution Steps

Factor out x^{2}.

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

Consider y^{4}-x^{4}. Rewrite y^{4}-x^{4} as \left(y^{2}\right)^{2}-\left(x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Reorder the terms.

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

Consider -x^{2}+y^{2}. Rewrite -x^{2}+y^{2} as y^{2}-x^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Reorder the terms.

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

Rewrite the complete factored expression.

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

Evaluate

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