Solve a^2x^3-a^6x

$$a ^ { 2 } x ^ { 3 } - a ^ { 6 } x$$

Factor

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

Solution Steps

Factor out a^{2}x.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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