Find The Sum: \left(2x^2 + 6x\right) + \left(x^2 - 5x + 7\right ]A. 3 X 2 + X + 7 3x^2 + X + 7 3 X 2 + X + 7 B. 7 X 2 − 11 X − 8 7x^2 - 11x - 8 7 X 2 − 11 X − 8 C. 8 X 2 − 3 X − 5 8x^2 - 3x - 5 8 X 2 − 3 X − 5 D. X 3 − 1 X 2 + 3 X^3 - 1x^2 + 3 X 3 − 1 X 2 + 3

Mar 13, 2025 by ADMIN 260 views

**Simplifying Algebraic Expressions: A Step-by-Step Guide**

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Understanding the Problem

In this article, we will delve into the world of algebraic expressions and explore the process of simplifying them. We will use a specific example to demonstrate the steps involved in combining like terms and simplifying expressions.

The Problem: Combining Like Terms

The problem we will be tackling is the following:

$\left(2x^2 + 6x\right) + \left(x^2 - 5x + 7\right)$

Our goal is to simplify this expression by combining like terms.

Step 1: Identify Like Terms

To simplify the expression, we need to identify the like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are:

$2x^2$ and $x^2$
$6x$ and $-5x$

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them. To do this, we add or subtract the coefficients of the like terms.

For the $x^2$ terms, we have $2x^2 + x^2 = 3x^2$
For the $x$ terms, we have $6x - 5x = x$

Step 3: Simplify the Expression

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

$\left(2x^2 + 6x\right) + \left(x^2 - 5x + 7\right) = 3x^2 + x + 7$

Conclusion

In this article, we have demonstrated the process of simplifying an algebraic expression by combining like terms. We have used a specific example to illustrate the steps involved in this process. By following these steps, you can simplify any algebraic expression and arrive at the correct solution.

Answer Key

The correct answer is:

A. $3x^2 + x + 7$

Common Mistakes to Avoid

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

Failing to identify like terms
Failing to combine like terms
Adding or subtracting terms incorrectly

Tips and Tricks

To simplify algebraic expressions, follow these tips and tricks:

Identify like terms carefully
Combine like terms systematically
Check your work carefully to avoid errors

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. These include:

Solving equations and inequalities
Graphing functions
Modeling real-world phenomena

Practice Problems

To practice simplifying algebraic expressions, try the following problems:

$\left(3x^2 + 2x\right) + \left(x^2 - 4x + 5\right)$
$\left(2x^2 - 3x + 1\right) + \left(x^2 + 2x - 3\right)$

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill in mathematics. By following the steps outlined in this article, you can simplify any algebraic expression and arrive at the correct solution. Remember to identify like terms carefully, combine like terms systematically, and check your work carefully to avoid errors. With practice and patience, you can become proficient in simplifying algebraic expressions and tackle even the most challenging problems.

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Frequently Asked Questions

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x^2$ and $x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression $2x^2 + 3x^2 + x$ , the like terms are $2x^2$ and $3x^2$ because they both have the variable $x$ raised to the power of 2.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, in the expression $2x^2 + 3x^2 + x$ , the like terms are $2x^2$ and $3x^2$ , which combine to give $5x^2$ .

Q: What is the order of operations for simplifying algebraic expressions?

A: The order of operations for simplifying algebraic expressions is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an algebraic expression with multiple variables?

A: To simplify an algebraic expression with multiple variables, identify the like terms and combine them as usual. For example, in the expression $2x^2y + 3x^2y + x$ , the like terms are $2x^2y$ and $3x^2y$ , which combine to give $5x^2y$ .

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change. For example, in the expression $2x + 3$ , $x$ is a variable and $3$ is a constant.

Q: How do I simplify an algebraic expression with a negative coefficient?

A: To simplify an algebraic expression with a negative coefficient, treat the negative sign as a separate term. For example, in the expression $-2x^2 + 3x^2$ , the like terms are $-2x^2$ and $3x^2$ , which combine to give $x^2$ .

Q: What is the final answer to the original problem?

A: The final answer to the original problem is:

$\left(2x^2 + 6x\right) + \left(x^2 - 5x + 7\right) = 3x^2 + x + 7$

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill in mathematics. By following the steps outlined in this article and answering the frequently asked questions, you can simplify any algebraic expression and arrive at the correct solution. Remember to identify like terms carefully, combine like terms systematically, and check your work carefully to avoid errors. With practice and patience, you can become proficient in simplifying algebraic expressions and tackle even the most challenging problems.