Q. 216 - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(\sqrt[3]{4x}+3\right)\left(\sqrt[3]{4x}-3\right)$

Step-by-Step Solution

Answer

By multiplying the expression we get, $\sqrt[3]{16x^2}-9.$

Step 1. Multiply the given expression

The given expression is $\left(\sqrt[3]{4x}+3\right)\left(\sqrt[3]{4x}-3\right).$

Multiply, using the Product of Conjugates Pattern

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

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} ={\left(\sqrt[3]{4x}\right)}^2-{\left(3\right)}^2 \\ =\sqrt[3]{16x^2}-9 \end{gathered}$$