Solve m^4-1

$$m ^ { 4 } - 1$$

Factor

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

Solution Steps

Rewrite m^{4}-1 as \left(m^{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).

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

Consider m^{2}-1. Rewrite m^{2}-1 as m^{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).

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

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

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

Evaluate

$$m^{4}-1$$