# How do you factor (x^8)-16?

${x}^{8} - 16 = {\left({x}^{4}\right)}^{2} - {4}^{2} = \left({x}^{4} - 4\right) \cdot \left({x}^{4} + 4\right) = \left({x}^{2} - 2\right) \cdot \left({x}^{2} + 2\right) \cdot \left[{\left({x}^{2} + 2\right)}^{2} - 4 {x}^{2}\right] = \left({x}^{2} - 2\right) \cdot \left({x}^{2} + 2\right) \cdot \left({x}^{2} + 2 - 2 x\right) \cdot \left({x}^{2} + 2 + 2 x\right)$