Question

Factor out the common factor. $$(x+3)^{2}-4(x+3)$$

   Factor out the common factor.
$$(x+3)^{2}-4(x+3)$$

College Algebra

College Algebra

Ron Larson 9th Edition

Chapter 0, Problem 8

Instant Answer

Solved by Expert Teresa Fuston

10/13/2021

Step 1

So, we can rewrite the given expression as $B^{2}-4B$. Show more…

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Factor out the common factor. $$(x+3)^{2}-4(x+3)$$

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Key Concepts

Common Factor

A common factor in an algebraic expression is a term that divides all parts of the expression without a remainder. Extracting this shared component simplifies the expression and is a key step in many algebraic manipulations, paving the way for further techniques such as solving equations or factoring polynomials completely.

Distributive Property

The distributive property is a fundamental principle in algebra which states that multiplying a sum by a number is equivalent to multiplying each addend individually by the number and then adding the results. This property is crucial when factoring out a common factor because the process involves reversing the distributive property to consolidate like terms.

Factorization

Factorization is the procedure of breaking down an algebraic expression into a product of simpler expressions or factors. This process not only simplifies complex expressions but also makes it easier to perform operations such as solving equations, simplifying expressions, and analyzing functional behavior in various branches of mathematics.

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