# How do you factor  x^6 + 16x^3 + 64?

We have that

${x}^{6} + 16 {x}^{3} + 64 = {\left({x}^{3}\right)}^{2} + 2 \cdot 8 \cdot {x}^{3} + {\left(8\right)}^{2} = {\left({x}^{3} + 8\right)}^{2}$

But ${x}^{3} + 8$ can be factored further as follows

${x}^{3} + 8 = {x}^{3} + {2}^{3} = \left(x + 2\right) \cdot \left({x}^{2} - 2 x + 4\right)$

Finally we get

${x}^{6} + 16 {x}^{3} + 64 = {\left(x + 2\right)}^{2} \cdot {\left({x}^{2} - 2 x + 4\right)}^{2}$