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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.462R (page 562)

In the following exercises, multiply each pair of conjugates using the Product of Conjugates.
$(13 a^{2} - 8 b^{4}) (13 a^{2} + 8 b^{4})$ .

Short Answer

Expert verified

The solution is $(13 a^{2} - 8 b^{4}) (13 a^{2} + 8 b^{4}) = 169 a^{4} - 64 b^{8}$ .

Step by step solution

01

Step 1

Recall the product of conjugates pattern $(a - b) (a + b) = a^{2} - b^{2}$ .

02

Step 2

Use $(a - b) (a + b) = a^{2} - b^{2}$ to find $(13 a^{2} - 8 b^{4}) (13 a^{2} + 8 b^{4})$ .

$\begin{array}{rcl} (13 a^{2} - 8 b^{4}) (13 a^{2} + 8 b^{4}) & = & {(13 a^{2})}^{2} - {(8 b^{4})}^{2} \\ = & 169 a^{4} - 64 b^{8} \end{array}$

So, $(13 a^{2} - 8 b^{4}) (13 a^{2} + 8 b^{4}) = 169 a^{4} - 64 b^{8}$ .

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