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

Step 1. Given information

Consider the given ploynomial.

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

Step 2. Formula used

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

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

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

Step 4. Write them as product of conjugate.

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Decision Maths

Geometry

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the difference of squares pattern, if possible.48m4n2-243n2

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

Probability and Statistics

Logic and Functions

Decision Maths

Geometry

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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