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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 190 (page 603)

In the following exercises, factor completely using the difference of squares pattern, if possible.
$48 m^{4} n^{2} - 243 n^{2}$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information

Consider the given ploynomial.

$48 m^{4} n^{2} - 243 n^{2}$

02

Step 2. Formula used

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

03

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

$48 m^{4} n^{2} - 23 n^{2} = 3 n^{2} (16 m^{4} - 81) = 3 n^{2} ({(4 m^{2})}^{2} - 9^{2}) = 3 n^{2} (4 m^{2} - 9) (4 m^{2} + 9)$

04

Step 4. Write them as product of conjugate.

$3 n^{2} (4 m^{2} - 9) (4 m^{2} + 9) = 3 n^{2} ({(2 m)}^{2} - 3^{2}) (4 m^{2} + 9) = 3 n^{2} (2 m - 3) (2 m + 3) (4 m^{2} + 9)$

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