Question

Facter each expression. $$a^{4}-b^{4}$$

   Facter each expression.
$$a^{4}-b^{4}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 73

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

Step 1

The difference of squares formula is $a^{2}-b^{2}=(a+b)(a-b)$. Show more…

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Facter each expression. $$a^{4}-b^{4}$$

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Key Concepts

Difference of Squares Factorization

This key concept involves recognizing patterns in algebraic expressions where one term is the square of another, resulting in the difference of two squares. The algebraic identity x² - y² = (x - y)(x + y) serves as the basis for factoring such expressions by rewriting them as a product of two binomials.

Iterative Factoring

Once an expression has been partially factored using a basic identity like the difference of squares, it is often possible to apply the same factoring techniques to the resulting factors. For example, if a factor itself is a difference of squares, it can be further decomposed, demonstrating how iterative application of identities simplifies complex polynomial expressions.

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