Q. 199 - Intermediate Algebra

Question

In the following exercises, multiply.

a.$(1+3\sqrt{10})(5-2\sqrt{10})$$(1+3\sqrt{10})(5-2\sqrt{10})$

b.$(2\sqrt[3]{x}+6)(\sqrt[3]{x}+1)$

Step-by-Step Solution

Answer

On multiplication, we get $-55+13\sqrt{10},2\sqrt[3]{x^2}+8\sqrt[3]{x}+6$ respectively

Part (a) Step 1: Given information

Given the expression, $(1+3\sqrt{10})(5-2\sqrt{10})$

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

Multiplying and simplifying, we get

$$\begin{gathered} (1+3\sqrt{10})(5-2\sqrt{10})=5-2\sqrt{10}+15\sqrt{10}-6\sqrt{(10{)}^2} \\ (1+3\sqrt{10})(5-2\sqrt{10})=5-2\sqrt{10}+15\sqrt{10}-6·10 \\ (1+3\sqrt{10})(5-2\sqrt{10})=5-60-2\sqrt{10}+15\sqrt{10} \\ (1+3\sqrt{10})(5-2\sqrt{10})=-55+13\sqrt{10} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $(2\sqrt[3]{x}+6)(\sqrt[3]{x}+1)$

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

Multiplying the terms and simplifying, we get

$$\begin{gathered} (2\sqrt[3]{x}+6)(\sqrt[3]{x}+1)=2\sqrt[3]{x^2}+2\sqrt[3]{x}+6\sqrt[3]{x}+6 \\ (2\sqrt[3]{x}+6)(\sqrt[3]{x}+1)=2\sqrt[3]{x^2}(2\sqrt[3]{x}+6\sqrt[3]{x})+6 \\ (2\sqrt[3]{x}+6)(\sqrt[3]{x}+1)=2\sqrt[3]{x^2}+8\sqrt[3]{x}+6 \end{gathered}$$