Q. 215 - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(\sqrt[3]{3x}+2\right)\left(\sqrt[3]{3x}-2\right)$

Step-by-Step Solution

Answer

By multiplying the expression we get, $\sqrt[3]{9x^2}-4.$

Step 1. Multiply the given expression

The given expression is $(\sqrt[3]{3x}+2)(\sqrt[3]{3x}-2).$

Multiply, using the Product of Conjugates Pattern

$$\begin{gathered} (\sqrt[3]{3x}+2)(\sqrt[3]{3x}-2) \\ ={\left(\sqrt[3]{3x}\right)}^2-{\left(2\right)}^2 \end{gathered}$$

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} ={\left(\sqrt[3]{3x}\right)}^2-{\left(2\right)}^2 \\ =\sqrt[3]{9x^2}-4 \end{gathered}$$