Factor by grouping. a x+4 x+a y+4 y

Name: Problem 43, Chapter 3: Intermediate Algebra
Uploaded: 2022-02-27T14:53:55-08:00
Duration: 19 s
Channel: Erika Bustos
Description: Factor by grouping. a x+4 x+a y+4 y

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Key Concepts

Factor by Grouping

Factor by grouping is a method used in algebra to factor expressions that have four or more terms. It involves grouping terms that have common factors, factoring out these common factors, and then applying the distributive property in reverse to factor the overall expression further.

Common Factors

The concept of common factors involves identifying elements, such as variables or coefficients, shared by two or more terms in an expression. By factoring out these common elements, the expression can be rewritten in a simpler, more manageable form.

Distributive Property

The distributive property is a fundamental principle in algebra that allows one to multiply a single term by a sum of terms. In factoring, this property is used in reverse to pull out a common factor from terms, effectively rewriting the expression as a product of factors.

Grouping Strategy

The grouping strategy involves dividing the expression into subsets of terms that each share a common factor. After factoring out the common factors in these groups, one often finds a common binomial factor, which can then be factored out further to simplify the expression even more.

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