# How do you factor 64+27t^3?

Apr 9, 2016

$\left(4 + 3 t\right) \left(16 - 12 t + 9 {t}^{2}\right)$

#### Explanation:

This is a $\textcolor{b l u e}{\text{ sum of 2 cubes " " and factors as follows }}$

 a^3 + b^3 = color(red)(|bar(ul(color(white)(a/a)color(black)((a+b)(a^2-ab+b^2)color(white)(a/a)|)))

For $64 + 27 {t}^{3} , \text{ a = 4" and b = 3t }$

substituting these values into the factored form.

$\Rightarrow 64 + 27 {t}^{3} = \left(4 + 3 t\right) \left(16 - 12 t + 9 {t}^{2}\right)$