Question

How would the expression x^2+27 be rewritten using sum of cubes?

Answer 1

Assuming the square is not a typo, one can write


$x^2+27=(x^{2/3})^3+3^3=(x^{2/3}+3)\bigg((x^{2/3})^2-3x^{2/3}+9\bigg)$

$=(x^{2/3}+3)\bigg(x^{4/3}-3x^{2/3}+9\bigg)$