How do you factor 125+t^3?

Apr 10, 2015

$\left(5 + t\right) \left(25 + 5 t + {t}^{2}\right)$

As color(blue)(a^3+b^3 can be written in the form
color(blue)((a+b)(a^2+ab+b^2) This is called the sum of cubes.

So, first of all write
$125 + {t}^{3}$ in the form ${5}^{3} + {t}^{3}$
Now, using the sum of cubes.

${5}^{3} + {t}^{3}$= $\left(5 + t\right) \left({5}^{2} + 5 t + {t}^{2}\right)$
=$\left(5 + t\right) \left(25 + 5 t + {t}^{2}\right)$