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

Step 1. Given information

Consider the given ploynomial.

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

Step 2. Formula used

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

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

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

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula used

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

Step 4. Write them as product of conjugate.

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In the following exercises, factor completely using the difference of squares pattern, if possible.162a4b2-32b2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula used

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

Step 4. Write them as product of conjugate.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Applied Mathematics

Calculus

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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