Problem 55 Write in factored form by factor... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 6: Problem 55

Write in factored form by factoring out the greatest common factor. $c(x+2)-d(x+2)$

Short Answer

Expert verified

$(x+2)(c - d)$

Step by step solution

- Identify the common factor

Look at the expression: $c(x+2) - d(x+2)$Notice that both terms, $c(x+2)$ and $d(x+2)$, contain the common factor $(x+2)$.

- Factor out the greatest common factor

Factor out the common term $(x+2)$ from the expression:$c(x+2) - d(x+2) = (x+2)(c - d)$

- Simplify the expression

Write down the factored form of the expression. The final factored form is:$(x+2)(c - d)$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Greatest Common Factor

The greatest common factor (GCF) is crucial when simplifying algebraic expressions. It is the largest factor that divides two or more terms.
To identify the GCF, look for common variables and constants in given terms.
In the expression provided: $c(x+2) - d(x+2)$, both terms share a common factor, $x+2$.
Therefore, the GCF is $x+2$.
Factoring out the GCF ensures that the expression is simplified in the most compact form possible.
This method is efficient in solving and manipulating algebraic equations.

Factored Form

Factoring is a technique used to express an equation as a product of its factors.
When you've identified the GCF, you can write the expression in 'factored form' by removing the common factor from each term.
For the given expression, $c(x+2) - d(x+2)$, the GCF $x+2$ is factored out:
$ c(x+2) - d(x+2) = (x+2)(c - d) $
This is the factored form.
In essence, factoring reduces the complexity of expressions and makes them easier to work with.
Recognizing factored form helps in further algebraic operations, such as solving equations.

Algebraic Expressions

Algebraic expressions are combinations of variables, constants, and operators (+, -, *, /).
Understanding how to manipulate these expressions is essential in algebra.
An expression like $c(x+2) - d(x+2)$ can be broken down and simplified by factoring.
By identifying common factors and writing the expression in factored form, we simplify our work.
This makes it much easier to handle, especially in complex algebra problems.
Mastery of algebraic expressions enables solving a wide array of mathematical problems efficiently.

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91影视

Write in factored form by factoring out the greatest common factor. \(c(x+2)-d(x+2)\)

Short Answer

Step by step solution

- Identify the common factor

- Factor out the greatest common factor

- Simplify the expression

Key Concepts

Greatest Common Factor

Factored Form

Algebraic Expressions

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