Solve m^4-k^4

$${ m }^{ 4 } - { k }^{ 4 }$$

Factor

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

Solution Steps

Rewrite m^{4}-k^{4} as \left(m^{2}\right)^{2}-\left(k^{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).

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

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

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

Rewrite the complete factored expression.

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

Evaluate

$$m^{4}-k^{4}$$