Question

Factor by grouping. $$ 2 a 3-a 2 b 2-2 a b+b 3 $$

   Factor by grouping.
$$
2 a 3-a 2 b 2-2 a b+b 3
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 6, Problem 93

Instant Answer

Solved by Expert James Kiss

01/29/2022

Step 1

Step 1: First, we group the terms as follows: $$ (2a^3 - a^2b^2) - (2ab - b^3) $$ Show more…

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Factor by grouping. $$ 2 a 3-a 2 b 2-2 a b+b 3 $$

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Key Concepts

Polynomial Factorization

Polynomial factorization is the process of expressing a polynomial as a product of simpler, lower-degree polynomials. This technique is fundamental in algebra and is used to simplify expressions, solve equations, and analyze polynomial behavior by breaking them down into their constituent factors.

Factoring by Grouping

Factoring by grouping is a specific method for polynomial factorization that involves rearranging and grouping terms in a polynomial to find common factors within each group. This approach is particularly useful when dealing with polynomials that have four or more terms, and it allows for the identification of a common binomial factor across different groups.

Greatest Common Factor

The Greatest Common Factor (GCF) is the largest factor that is common to all the terms in a polynomial. Extracting the GCF simplifies the polynomial expression and makes subsequent factoring steps, such as grouping or applying special factorization formulas, more straightforward and efficient.

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