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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.235. (page 537)

Multiply each pair of conjugates using the product of the conjugates pattern.
$(p + \frac{4}{5} q) (p - \frac{4}{5} q)$

Short Answer

Expert verified

The solution is $p^{2} - \frac{16}{25} q^{2}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $(p + \frac{4}{5} q) (p - \frac{4}{5} q)$ .

02

Step 2. Simplify the expression by using the difference of squares a+ba-b=a2-b2.

Solve it as follows:

$(p + \frac{4}{5} q) (p - \frac{4}{5} q) = {(p)}^{2} - {(\frac{4}{5} q)}^{2} 鈬� p^{2} - \frac{16}{25} q^{2}$

03

Step 3. Simplified expression.

Hence, the required expression is $p^{2} - \frac{16}{25} q^{2}$ .

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