Question

Factor x^3 + 1/8
thank you

Answer 1

`\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ x^3+\cfrac{1}{8}\implies x^3+\cfrac{1^3}{2^3}\implies x^3+\left( \cfrac{1}{2} \right)^3~\hfill \stackrel{\textit{let's just for a second make}}{\cfrac{1}{2}=a} \\\\\\ x^3+a^3\implies (x+a)(x^2-ax+a^2)\implies \left( x+(1)/(2) \right)\left( x^2-(x)/(2)+(1)/(4) \right)`