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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q.525 (page 853)

In the following exercises, multiply
$a) (3 鈥� 鈭� 鈥� 2 \sqrt{7}) (5 鈥� 鈭� 鈥� 4 鈥� \sqrt{7}) b) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$

Short Answer

Expert verified

Simplifying,

$a) (3 鈥� 鈭� 鈥� 2 \sqrt{7}) (5 鈥� 鈭� 鈥� 4 鈥� \sqrt{7}) = 71 - 22 \sqrt{7} b) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3) = {(\sqrt[3]{x})}^{2} - 8 \sqrt[3]{x} + 15$

Step by step solution

01

Step 1. Given information

We have given,

a) (3 鈥� 鈭� 鈥� 2 \sqrt{7}) (5 鈥� 鈭� 鈥� 4 鈥� \sqrt{7}) b) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)

02

Step 2. Concept

Here we will going to use FOIL method,

$(a + b) (c + d) = a c + a d + b c + b d$

and radical rules,

$\sqrt[n]{a} \sqrt[n]{b} = \sqrt[n]{a b}$

$\sqrt[n]{a^{n}} = a$

03

Part (a) Step 1. Explanation

We have,

$鈥� (3 鈥� 鈭� 鈥� 2 \sqrt{7}) (5 鈥� 鈭� 鈥� 4 鈥� \sqrt{7})$

Using FOIL method,

$3 路鈥� 5 + 3 (- 4 \sqrt{7}) - 2 \sqrt{7} 路鈥� 5 - 2 \sqrt{7} (- 4 \sqrt{7})$

Using radical rule,

$15 - 12 \sqrt{7} - 10 \sqrt{7} + 56$

$鈬� 71 - 22 \sqrt{7}$

04

Part (a) Step 2. Conclusion

Hence, multiplying and simplifying $(3 - 2 \sqrt{7}) (5 - 4 \sqrt{7})$ we will get,

$71 - 22 \sqrt{7}$

05

Part (b) Step. Explanation

We have,

$(\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$

Using FOIL method,

$\sqrt[3]{x} \sqrt[3]{x} + \sqrt[3]{x} (- 3) - 5 \sqrt[3]{x} - 5 (- 3)$

Using radical rule,

${(\sqrt[3]{x})}^{2} - 8 \sqrt[3]{x} + 15$

06

Part (b) Step 2. Conclusion

Hence, multiplying and simplifying $(\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$ we will get,

${(\sqrt[3]{x})}^{2} - 8 \sqrt[3]{x} + 15$ .

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Most popular questions from this chapter

In the following exercises, simplify using absolute value signs as needed. $\sqrt{147 m^{7} n^{11}}, \sqrt[3]{48 x^{6} y^{7}}, \sqrt[4]{32 x^{5} y^{4}}$

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[5]{64}$ , b. $\sqrt[3]{256}$

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{28 q^{6}}{225}}$

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$(a) \sqrt[3]{a} (b) (\sqrt[4]{21 v})^{3} (c) \sqrt[4]{{(\frac{2 x y}{5 z})}^{2}}$

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