Solve x^2*x^2-1

$${ x }^{ 2 } \times { x }^{ 2 } -1$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$x^{4}-1$$

Rewrite x^{4}-1 as \left(x^{2}\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

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

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

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

Evaluate

$$x^{4}-1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$x^{4}-1$$