Solve 125x^6-5x^2y^4

$$125 x ^ { 6 } - 5 x ^ { 2 } y ^ { 4 }$$

Factor

$$5x^{2}\left(5x^{2}-y^{2}\right)\left(5x^{2}+y^{2}\right)$$

Solution Steps

Factor out 5.

$$5\left(25x^{6}-x^{2}y^{4}\right)$$

Consider 25x^{6}-x^{2}y^{4}. Factor out x^{2}.

$$x^{2}\left(25x^{4}-y^{4}\right)$$

Consider 25x^{4}-y^{4}. Rewrite 25x^{4}-y^{4} as \left(5x^{2}\right)^{2}-\left(y^{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).

$$\left(5x^{2}-y^{2}\right)\left(5x^{2}+y^{2}\right)$$

Rewrite the complete factored expression.

$$5x^{2}\left(5x^{2}-y^{2}\right)\left(5x^{2}+y^{2}\right)$$

Evaluate

$$125x^{6}-5x^{2}y^{4}$$