Chapter 6: Q 188 (page 601)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

Consider the given ploynomial

$m^{4} - n^{4}$

Step 2. Formula used

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

Step 3. Write the polynomial as squares.

Write the polynomial as perfect squared form.

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

Write them as product of conjugate.

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

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.
$m^{4} - n^{4}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula used

Step 3. Write the polynomial as squares.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Geometry

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the difference of squares pattern, if possible.m4-n4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula used

Step 3. Write the polynomial as squares.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Geometry

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

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