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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.461R (page 562)

In the following exercises, multiply each pair of conjugates using the Product of Conjugates.
$(12 x^{3} - 7 y^{2}) (12 x^{3} + 7 y^{2})$ .

Short Answer

Expert verified

The solution is $(12 x^{3} - 7 y^{2}) (12 x^{3} + 7 y^{2}) = 144 x^{6} - 49 y^{4}$ .

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 $(12 x^{3} - 7 y^{2}) (12 x^{3} + 7 y^{2})$ .

$\begin{array}{rcl} (12 x^{3} - 7 y^{2}) (12 x^{3} + 7 y^{2}) & = & {(12 x^{3})}^{2} - {(7 y^{2})}^{2} \\ = & 144 x^{6} - 49 y^{4} \end{array}$

So, $(12 x^{3} - 7 y^{2}) (12 x^{3} + 7 y^{2}) = 144 x^{6} - 49 y^{4}$ .

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