Factor. x(a^2-b^2)-y(a^2-b^2)

Name: Problem 84, Chapter 10: Prealgebra and Introductory Algebra
Uploaded: 2020-06-26T16:26:59-08:00
Duration: 1 min 13 s
Channel: Jason Taylor-Pestell
Description: Factor. x(a^2-b^2)-y(a^2-b^2)

step 1 All right, so 84 is very similar to 83. If you watch that video, we'll begin by looking for the

Question

Factor. $$x\left(a^{2}-b^{2}\right)-y\left(a^{2}-b^{2}\right)$$

   Factor.
$$x\left(a^{2}-b^{2}\right)-y\left(a^{2}-b^{2}\right)$$

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 10, Problem 84

Instant Answer

Solved by Expert Jason Taylor-Pestell

06/26/2020

Step 1

In this case, the common factor is $(a^{2}-b^{2})$. We factor this out from both terms. So, we have: $$x(a^{2}-b^{2})-y(a^{2}-b^{2}) = (a^{2}-b^{2})(x-y)$$ Show more…

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Factor. $$x\left(a^{2}-b^{2}\right)-y\left(a^{2}-b^{2}\right)$$

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Key Concepts

Common Factor Extraction

This concept involves identifying and factoring out a term that is common to all parts of an expression. By extracting the common factor, the expression is rewritten in a simpler product form, which can simplify further operations such as solving equations or additional factoring.

Difference of Squares

This is a specific algebraic identity where an expression of the form a² - b² can be rewritten as (a - b)(a + b). Recognizing and applying this pattern allows for the further factorization of expressions that exhibit this structure.

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