Solve r^4-16k^4

$$r ^ { 4 } - 16 k ^ { 4 }$$

Factor

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

Solution Steps

Rewrite r^{4}-16k^{4} as \left(r^{2}\right)^{2}-\left(4k^{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).

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

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

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

Rewrite the complete factored expression.

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

Evaluate

$$r^{4}-16k^{4}$$