Perform The Operation:$\left(-8x^2 + 5x + 3\right) + \left(6x + 6\right$\]

Introduction

Algebraic operations are a fundamental aspect of mathematics, and understanding how to perform them is crucial for solving equations and manipulating expressions. In this article, we will focus on performing the operation of adding two algebraic expressions, specifically the expression $\left(-8x^2 + 5x + 3\right) + \left(6x + 6\right)$. We will break down the process into manageable steps and provide a clear explanation of each step.

Understanding the Problem

The given problem involves adding two algebraic expressions, which are $\left(-8x^2 + 5x + 3\right)$ and $\left(6x + 6\right)$. To add these expressions, we need to combine like terms, which means combining terms that have the same variable and exponent.

Step 1: Identify Like Terms

The first step in adding the expressions is to identify like terms. In the expression $\left(-8x^2 + 5x + 3\right)$, we have three terms: $-8x^2$, $5x$, and $3$. In the expression $\left(6x + 6\right)$, we have two terms: $6x$ and $6$. We can see that the term $5x$ in the first expression is like the term $6x$ in the second expression, as they both have the same variable and exponent.

Step 2: Combine Like Terms

Now that we have identified like terms, we can combine them. We will combine the terms $5x$ and $6x$ to get $11x$. We will also combine the constant terms $3$ and $6$ to get $9$.

Step 3: Simplify the Expression

After combining like terms, we can simplify the expression by writing it in the standard form. The expression $\left(-8x^2 + 5x + 3\right) + \left(6x + 6\right)$ can be simplified to $\left(-8x^2 + 11x + 9\right)$.

Conclusion

In this article, we have performed the operation of adding two algebraic expressions, specifically the expression $\left(-8x^2 + 5x + 3\right) + \left(6x + 6\right)$. We have broken down the process into manageable steps and provided a clear explanation of each step. By following these steps, we have successfully combined like terms and simplified the expression to get the final result of $\left(-8x^2 + 11x + 9\right)$.

Tips and Tricks

• When adding algebraic expressions, it is essential to identify like terms and combine them.
• When combining like terms, make sure to add the coefficients of the terms.
• When simplifying the expression, make sure to write it in the standard form.

Real-World Applications

Algebraic operations are used in various real-world applications, such as:

• Science and Engineering: Algebraic operations are used to solve equations and manipulate expressions in scientific and engineering applications.
• Computer Science: Algebraic operations are used in computer science to solve equations and manipulate expressions in programming languages.
• Finance: Algebraic operations are used in finance to solve equations and manipulate expressions in financial models.

Common Mistakes

• Not identifying like terms: Failing to identify like terms can lead to incorrect results.
• Not combining like terms: Failing to combine like terms can lead to incorrect results.
• Not simplifying the expression: Failing to simplify the expression can lead to incorrect results.

Conclusion

Q: What are algebraic operations?

A: Algebraic operations are mathematical operations that involve manipulating algebraic expressions, such as adding, subtracting, multiplying, and dividing.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $3x$ are like terms because they both have the variable $x$ and the exponent $1$.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the terms. For example, if you have the terms $2x$ and $3x$, you can combine them by adding the coefficients: $2x + 3x = 5x$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The order of operations is:

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

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and eliminate any unnecessary parentheses or brackets. For example, if you have the expression $2x + 3x + 4$, you can simplify it by combining the like terms: $2x + 3x + 4 = 5x + 4$.

Q: What are some common algebraic operations?

A: Some common algebraic operations include:

• Adding and subtracting like terms
• Multiplying and dividing expressions
• Evaluating expressions with parentheses and brackets
• Simplifying expressions by combining like terms

Q: How do I use algebraic operations in real-world applications?

A: Algebraic operations are used in a wide range of real-world applications, including:

• Science and engineering: Algebraic operations are used to solve equations and manipulate expressions in scientific and engineering applications.
• Computer science: Algebraic operations are used in computer science to solve equations and manipulate expressions in programming languages.
• Finance: Algebraic operations are used in finance to solve equations and manipulate expressions in financial models.

Q: What are some common mistakes to avoid when performing algebraic operations?

A: Some common mistakes to avoid when performing algebraic operations include:

• Not identifying like terms
• Not combining like terms
• Not simplifying the expression
• Not following the order of operations

Q: How can I practice algebraic operations?

A: You can practice algebraic operations by working through examples and exercises in a textbook or online resource. You can also try solving problems on your own or with a partner to help reinforce your understanding of the concepts.

Conclusion

In conclusion, algebraic operations are a fundamental aspect of mathematics, and understanding how to perform them is essential for solving equations and manipulating expressions. By following the steps outlined in this article, you can successfully perform algebraic operations and apply them to real-world applications.