Q. 197 - Intermediate Algebra

Question

In the following exercises, multiply. 

a.$(9-3\sqrt{2})(6+4\sqrt{2})$

b.$(\sqrt[3]{x}-3)(\sqrt[3]{x}+1)$

Step-by-Step Solution

Answer

On multiplication, we get $30+18\sqrt{2},\sqrt[3]{x^2}-2\sqrt[3]{x}-3$ respectively

Part (a) Step 1: Given information

Given the expression $(9-3\sqrt{2})(6+4\sqrt{2}),(\sqrt[3]{x}-3)(\sqrt[3]{x}+1)$

Part (a) Step 2: Multiplying the terms and simplifying

Multiplying and simplifying we get

$$\begin{gathered} (9-3\sqrt{2})(6+4\sqrt{2})=54+36\sqrt{2}-18\sqrt{2}-12\sqrt{(2{)}^2} \\ (9-3\sqrt{2})(6+4\sqrt{2})=54+36\sqrt{2}-18\sqrt{2}-12·2 \\ (9-3\sqrt{2})(6+4\sqrt{2})=(54-24)+(36\sqrt{2}-18\sqrt{2}) \\ (9-3\sqrt{2})(6+4\sqrt{2})=30+18\sqrt{2} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $(\sqrt[3]{x}-3)(\sqrt[3]{x}+1)$

Part (b) Step 2: Multiplying the terms and simplifying

Multiplying the terms and simplifying, we get

$$\begin{gathered} (\sqrt[3]{x}-3)(\sqrt[3]{x}+1)=\sqrt[3]{x^2}+\sqrt[3]{x}-3\sqrt[3]{x}-3 \\ (\sqrt[3]{x}-3)(\sqrt[3]{x}+1)=\sqrt[3]{x^2}+(\sqrt[3]{x}-3\sqrt[3]{x})-3 \\ (\sqrt[3]{x}-3)(\sqrt[3]{x}+1)=\sqrt[3]{x^2}-2\sqrt[3]{x}-3 \end{gathered}$$