Solve x^3-2x^3+x

$${ x }^{ 3 } -2 { x }^{ 3 } +x$$

Factor

$$x\left(-x-1\right)\left(x-1\right)$$

Solution Steps

Factor out x.

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

Consider x^{2}-2x^{2}+1. Multiply and combine like terms.

$$-x^{2}+1$$

Consider -x^{2}+1. Rewrite -x^{2}+1 as 1^{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).

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

Reorder the terms.

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

Rewrite the complete factored expression.

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

Evaluate

$$x-x^{3}$$

Solution Steps

Combine x^{3} and -2x^{3} to get -x^{3}.

$$-x^{3}+x$$