Solve k^4-16

$$k ^ { 4 } - 16$$

Factor

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

Solution Steps

Rewrite k^{4}-16 as \left(k^{2}\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

$$\left(k-2\right)\left(k+2\right)$$

Rewrite the complete factored expression. Polynomial k^{2}+4 is not factored since it does not have any rational roots.

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

Evaluate

$$k^{4}-16$$