(x+2)^2-5(x+2)

Jasonbradley

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Jun 16, 2024

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Factoring and Simplifying the Expression (x+2)² - 5(x+2)

This expression can be simplified and factored using algebraic techniques. Let's break down the process step by step.

Understanding the Expression

The expression (x+2)² - 5(x+2) involves:

• A squared term: (x+2)² represents the product of (x+2) multiplied by itself.
• A linear term: -5(x+2) is a simple multiplication of -5 and (x+2).

Factoring by Grouping

We can simplify the expression by factoring out the common factor (x+2):

1. Identify the common factor: Notice that both terms in the expression contain (x+2).
2. Factor out the common factor:
   • (x+2)² = (x+2)(x+2)
   • -5(x+2) = -5(x+2)
3. Rewrite the expression: (x+2)(x+2) - 5(x+2) = (x+2)[(x+2) - 5]

Simplifying the Expression

Now we can simplify the expression inside the brackets:

• (x+2)[(x+2) - 5] = (x+2)(x - 3)

Final Result

The simplified and factored form of the expression (x+2)² - 5(x+2) is (x+2)(x-3).

Applications

This type of expression is frequently encountered in algebra and calculus. Understanding how to factor and simplify such expressions is crucial for solving equations, finding roots, and performing various mathematical operations.