Question

How do you factor $64x^3+27$?

Answer 1

Find the factor of $64x^3+27$:

Given, that the expression is $64x^3+27$.

The algebraic identity is$a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$.

The expression $64x^3+27$ can be written as ${\left(4x\right)}^3+3^3$:

$\begin{array}{rcl}{\left(4x\right)}^3+3^3& =& \left(4x+3\right)\left\{{\left(4x\right)}^2-4x·3+3^2\right\}\left[a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)\right]\\ & =& \left(4x+3\right)\left(16x^2-12x+9\right)\end{array}$

Therefore, the factor of $64x^3+27$ is $\left(4x+3\right)\left(16x^2-12x+9\right)$.