Solve x^3-w^4x^3

$$x ^ { 3 } - w ^ { 4 } x ^ { 3 }$$

Factor

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

Solution Steps

Factor out x^{3}.

$$x^{3}\left(1-w^{4}\right)$$

Consider 1-w^{4}. Rewrite 1-w^{4} as 1^{2}-\left(-w^{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).

$$\left(1+w^{2}\right)\left(1-w^{2}\right)$$

Reorder the terms.

$$\left(w^{2}+1\right)\left(-w^{2}+1\right)$$

Consider -w^{2}+1. Rewrite -w^{2}+1 as 1^{2}-w^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-w\right)\left(1+w\right)$$

Reorder the terms.

$$\left(-w+1\right)\left(w+1\right)$$

Rewrite the complete factored expression. Polynomial w^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

$$x^{3}\left(1-w^{4}\right)$$