Chapter 8.7, Problem 37PPE

To determine

To factor the expression $27w^2-12$ .

Answer to Problem 37PPE

  $27w^2-12=3\left(3w-2\right)\left(3w+2\right)$

Explanation of Solution

Given:

  $27w^2-12$

Concept used:

  $\left(a+b\right)\left(a-b\right)=a^2-b^2$

Calculation:

  $\begin{array}{l}27w^2-12=3\left(9w^2-4\right)\\ =3\left[{\left(3w\right)}^2-2^2\right]\\ =3\left(3w-2\right)\left(3w+2\right)\end{array}$