# Question #3fdac

Jan 20, 2015

The key is to use powers to express your two terms.

Your first term can be written as $8 = {2}^{3}$, and your second term can be written as ${z}^{6} = {\left({z}^{2}\right)}^{3}$, which makes your expression

${2}^{3} + {\left({z}^{2}\right)}^{3} = \left(2 + {z}^{2}\right) \left({2}^{2} - 2 \cdot {z}^{2} + {\left({z}^{2}\right)}^{2}\right)$

${2}^{3} + {\left({z}^{2}\right)}^{3} = \left(2 + {z}^{2}\right) \left(4 - 2 {z}^{2} + {z}^{4}\right)$

I've used the fact that

${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$