Solve x^4+x^2-x^2(x^2+1)

$$x ^ { 4 } + x ^ { 2 } - x ^ { 2 } ( x ^ { 2 } + 1 )$$

Evaluate

$$0$$

Solution Steps

Use the distributive property to multiply x^{2} by x^{2}+1.

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

To find the opposite of x^{4}+x^{2}, find the opposite of each term.

$$x^{4}+x^{2}-x^{4}-x^{2}$$

Combine x^{4} and -x^{4} to get 0.

$$x^{2}-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$0$$

Factor

$$0$$

Solution Steps

Factor out x^{2}+1 in x^{4}+x^{2}.

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

Factor out common term x^{2} by using distributive property.

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

Consider -\left(x^{2}+1\right)+x^{2}+1. Simplify.

$$0$$