# How do you factor 316 - 343t^3?

Oct 5, 2017

$\left(6 - 7 t\right) \left(36 + 42 t + {t}^{2}\right)$

#### Explanation:

Assuming the question as $216 - 343 {t}^{3}$ as suggested by Mr George,
a^3-b^3=(a-b)(a^2+ab+b^2
${6}^{3} = 216$ Hence $a = 6$ & ${7}^{3} = 343$ and hence $b = 7$.
The factors are
$\left(6 - 7 t\right) \left({6}^{2} + \left(6 \cdot 7 t\right) + {\left(7 t\right)}^{2}\right)$
$\left(6 - 7 t\right) \left(36 + 42 t + {t}^{2}\right)$