Factor. a(x^2-4)+b(x^2-4)

Name: Problem 83, Chapter 10: Prealgebra and Introductory Algebra
Uploaded: 2020-06-26T16:25:27-08:00
Duration: 1 min 57 s
Channel: Jason Taylor-Pestell
Description: Factor. a(x^2-4)+b(x^2-4)

step 1 All right, so number 83 is a little bit different than some of the other problems that we've bee

Question

Factor. $$a\left(x^{2}-4\right)+b\left(x^{2}-4\right)$$

   Factor.
$$a\left(x^{2}-4\right)+b\left(x^{2}-4\right)$$

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 10, Problem 83

Instant Answer

Solved by Expert Jason Taylor-Pestell

06/26/2020

Step 1

We notice that both terms have the binomial $x^{2}-4$ in common. So, we factor out $x^{2}-4$ from both terms. This gives us: $$(x^{2}-4)(a+b)$$ Show more…

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Factor. $$a\left(x^{2}-4\right)+b\left(x^{2}-4\right)$$

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Key Concepts

Common Factor Extraction

This technique involves identifying and removing factors that are common to each term in an expression. It simplifies expressions by transforming sums of products into a single product, as seen when both terms share the factor (x² - 4).

Distributive Property

This property states that a common factor multiplied by a sum is equal to the sum of the common factor multiplied by each addend individually. It serves as the foundation for both expanding and factoring expressions within algebra.

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