# How do you factor x^3+1?

${x}^{3} + 1 = {x}^{3} + {1}^{3}$
color(blue)(a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Hence ${x}^{3} + {1}^{3} = \left(x + 1\right) \left({x}^{2} - \left(x \cdot 1\right) + {1}^{2}\right)$
 = color(green)((x + 1)(x^2 - x + 1)#