How do you factor 27-t^3?

Oct 9, 2015

$\left(3 - t\right) \left(9 + 3 t + {t}^{2}\right)$
$27 - {t}^{3} \implies$ use difference of cubes formula:
${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right) \implies$ so in this case we have:
$\left({3}^{3} - {t}^{3}\right) = \left(3 - t\right) \left(9 + 3 t + {t}^{2}\right)$