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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 5: Q.232. (page 537)

Multiply each pair of conjugates using the product of the conjugates pattern.
$(9 c - 2 d) (9 c + 2 d)$

Short Answer

Expert verified

The solution is $81 c^{2} - 4 d^{2}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $(9 c - 2 d) (9 c + 2 d)$ .

02

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

Solve it as follows:

$(9 c - 2 d) (9 c + 2 d) = {(9 c)}^{2} - {(2 d)}^{2} \Rightarrow 81 c^{2} - 4 d^{2}$

03

Step 3. Simplified expression.

Hence, the required expression is $81 c^{2} - 4 d^{2}$ .

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