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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q 189 (page 603)

In the following exercises, factor completely using the difference of squares pattern, if possible.
$162 a^{4} b^{2} - 32 b^{2}$

Short Answer

Expert verified

The complete factor of ploynomial is $2 b^{2} (3 a - 2) (3 a + 2) (9 a^{2} + 4)$

Step by step solution

01

Step 1. Given information

Consider the given ploynomial.

$162 a^{4} b^{2} - 32 b^{2}$

02

Step 2. Formula used

$a^{2} - b^{2} = (a + b) (a - b)$

03

Step 3. Find the factor using difference of square pattern.

$162 a^{4} b^{2} - 32 b^{2} = 2 b^{2} (81 a^{4} - 16) = 2 b^{2} ({(9 a^{2})}^{2} - 4^{2}) = 2 b^{2} (9 a^{2} - 4) (9 a^{2} + 4)$

04

Step 4. Write them as product of conjugate.

$2 b^{2} (9 a^{2} - 4) (9 a^{2} + 4) = 2 b^{2} ({(3 a)}^{2} - 2^{2}) (9 a^{2} + 4) = 2 b^{2} (3 a - 2) (3 a + 2) (9 a^{2} + 4)$

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