Simplify: $\left(5x - 3x^2 - 24\right) + \left(4x^2 - 6 - 4x\right$\]

Feb 26, 2025 by ADMIN 70 views

Simplifying Algebraic Expressions: A Step-by-Step Guide

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Introduction

Simplifying algebraic expressions is a fundamental concept in mathematics that helps us to rewrite complex expressions in a more manageable form. It is an essential skill for students of mathematics, science, and engineering. In this article, we will explore the process of simplifying algebraic expressions, focusing on the given expression: $\left(5x - 3x^2 - 24\right) + \left(4x^2 - 6 - 4x\right)$ . We will break down the steps involved in simplifying this expression and provide a clear understanding of the concepts involved.

Understanding the Expression

The given expression is a combination of two algebraic expressions, each enclosed in parentheses. To simplify this expression, we need to combine like terms, which involves adding or subtracting terms with the same variable and exponent.

Like Terms

Like terms are terms that have the same variable and exponent. In the given expression, we can identify the following like terms:

$5x$ and $-4x$
$-3x^2$ and $4x^2$
$-24$ and $-6$

Simplifying the Expression

To simplify the expression, we need to combine like terms. We will start by combining the like terms identified in the previous section.

Combining Like Terms

We will combine the like terms as follows:

$5x$ and $-4x$ can be combined to get $x$ .
$-3x^2$ and $4x^2$ can be combined to get $x^2$ .
$-24$ and $-6$ can be combined to get $-30$ .

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by adding the remaining terms.

$\left(5x - 3x^2 - 24\right) + \left(4x^2 - 6 - 4x\right)$

$= x^2 + x - 30$

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics that helps us to rewrite complex expressions in a more manageable form. By combining like terms and simplifying the expression, we can arrive at a simplified form of the given expression. In this article, we have explored the process of simplifying the expression $\left(5x - 3x^2 - 24\right) + \left(4x^2 - 6 - 4x\right)$ and provided a clear understanding of the concepts involved.

Tips and Tricks

When simplifying algebraic expressions, it is essential to identify like terms and combine them.
Use the distributive property to simplify expressions with multiple terms.
Simplify expressions by combining like terms and eliminating any unnecessary terms.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in mathematics, science, and engineering. Some of the real-world applications of simplifying algebraic expressions include:

Physics and Engineering: Simplifying algebraic expressions is essential in physics and engineering to solve problems involving motion, forces, and energy.
Computer Science: Simplifying algebraic expressions is used in computer science to optimize algorithms and solve complex problems.
Economics: Simplifying algebraic expressions is used in economics to model economic systems and make predictions about economic trends.

Common Mistakes to Avoid

When simplifying algebraic expressions, there are several common mistakes to avoid:

Not identifying like terms: Failing to identify like terms can lead to incorrect simplification of the expression.
Not combining like terms: Failing to combine like terms can lead to incorrect simplification of the expression.
Not eliminating unnecessary terms: Failing to eliminate unnecessary terms can lead to incorrect simplification of the expression.

Final Thoughts

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Introduction

Simplifying algebraic expressions is a fundamental concept in mathematics that helps us to rewrite complex expressions in a more manageable form. In our previous article, we explored the process of simplifying the expression $\left(5x - 3x^2 - 24\right) + \left(4x^2 - 6 - 4x\right)$ and provided a clear understanding of the concepts involved. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to identify like terms. Like terms are terms that have the same variable and exponent.

Q: How do I identify like terms in an algebraic expression?

A: To identify like terms, look for terms that have the same variable and exponent. For example, in the expression $2x + 3x$ , the terms $2x$ and $3x$ are like terms because they have the same variable ( $x$ ) and exponent (1).

Q: What is the next step after identifying like terms?

A: After identifying like terms, the next step is to combine like terms. Combining like terms involves adding or subtracting the coefficients of the like terms.

Q: How do I combine like terms in an algebraic expression?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, in the expression $2x + 3x$ , the coefficients of the like terms are 2 and 3. Combining these coefficients gives us $5x$ .

Q: What is the final step in simplifying an algebraic expression?

A: The final step in simplifying an algebraic expression is to eliminate any unnecessary terms. Unnecessary terms are terms that do not contribute to the value of the expression.

Q: How do I eliminate unnecessary terms in an algebraic expression?

A: To eliminate unnecessary terms, look for terms that are equal to zero. If a term is equal to zero, it can be eliminated from the expression.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

Not identifying like terms
Not combining like terms
Not eliminating unnecessary terms

Q: How do I know if an algebraic expression is simplified?

A: An algebraic expression is simplified if it has no like terms and no unnecessary terms.

Q: Can you provide an example of a simplified algebraic expression?

A: Yes, an example of a simplified algebraic expression is $2x + 3y - 4z$ . This expression is simplified because it has no like terms and no unnecessary terms.

Q: How do I apply simplifying algebraic expressions in real-world scenarios?

A: Simplifying algebraic expressions is used in a variety of real-world scenarios, including physics and engineering, computer science, and economics. In these fields, simplifying algebraic expressions helps to solve complex problems and make predictions about real-world phenomena.