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

Introduction

In algebra, performing operations on expressions is a crucial skill that helps us simplify complex equations and solve problems efficiently. In this article, we will focus on performing the operation $\left(-8x^2 + 3\right) + \left(x^2 + 3x - 8\right)$, which involves combining like terms and simplifying the resulting expression.

Understanding the Problem

The given problem involves adding two algebraic expressions: $\left(-8x^2 + 3\right)$ and $\left(x^2 + 3x - 8\right)$. To perform this operation, we need to combine like terms, which means adding or subtracting terms that have the same variable and exponent.

Step 1: Identify Like Terms

To identify like terms, we need to look for terms that have the same variable and exponent. In this case, we have two terms with the variable $x^2$: $-8x^2$ and $x^2$. We also have two terms with the variable $x$: $3x$ and $0x$ (which is not explicitly written, but we can assume it's there).

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them by adding or subtracting their coefficients. In this case, we have:

• $-8x^2 + x^2 = -7x^2$
• $3x + 0x = 3x$

Step 3: Simplify the Expression

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

$\left(-8x^2 + 3\right) + \left(x^2 + 3x - 8\right) = -7x^2 + 3x - 5$

Conclusion

In this article, we performed the operation $\left(-8x^2 + 3\right) + \left(x^2 + 3x - 8\right)$ by combining like terms and simplifying the resulting expression. We identified the like terms, combined them, and simplified the expression to get the final result: $-7x^2 + 3x - 5$. This problem demonstrates the importance of combining like terms and simplifying expressions in algebra.

Tips and Tricks

• When combining like terms, make sure to add or subtract their coefficients.
• When simplifying expressions, make sure to combine like terms and eliminate any unnecessary terms.
• Practice, practice, practice! The more you practice combining like terms and simplifying expressions, the more comfortable you will become with these skills.

Common Mistakes

• Failing to identify like terms: Make sure to carefully examine the expression and identify the like terms.
• Failing to combine like terms: Make sure to add or subtract the coefficients of the like terms.
• Failing to simplify the expression: Make sure to combine like terms and eliminate any unnecessary terms.

Real-World Applications

Combining like terms and simplifying expressions is an essential skill in algebra that has many real-world applications. For example:

• In physics, combining like terms and simplifying expressions is used to solve problems involving motion, energy, and momentum.
• In engineering, combining like terms and simplifying expressions is used to design and optimize systems, such as electrical circuits and mechanical systems.
• In economics, combining like terms and simplifying expressions is used to analyze and model economic systems, such as supply and demand curves.

Conclusion

Introduction

In our previous article, we discussed how to perform the operation $\left(-8x^2 + 3\right) + \left(x^2 + 3x - 8\right)$ by combining like terms and simplifying the resulting expression. In this article, we will answer some frequently asked questions about performing algebraic operations.

Q: What are like terms?

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

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable and exponent. You can do this by examining the expression and grouping terms that have the same variable and exponent together.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms involves adding or subtracting the coefficients of like terms, while simplifying an expression involves combining like terms and eliminating any unnecessary terms.

Q: How do I combine like terms?

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

Q: What is the order of operations when simplifying an expression?

A: The order of operations when simplifying an expression is:

1. Parentheses: Evaluate any 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 with multiple variables?

A: To simplify an expression with multiple variables, you need to combine like terms and eliminate any unnecessary terms. For example, if you have the expression $2x^2y + 3x^2y$, you can combine the like terms by adding the coefficients: $2x^2y + 3x^2y = 5x^2y$.

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

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

• Failing to identify like terms
• Failing to combine like terms
• Failing to simplify the expression
• Adding or subtracting terms that are not like terms

Q: How do I check my work when simplifying an expression?

A: To check your work when simplifying an expression, you can plug in a value for the variable and evaluate the expression. If the expression simplifies to the correct value, then you know that your work is correct.

Conclusion

In conclusion, performing algebraic operations, such as combining like terms and simplifying expressions, is an essential skill in algebra that has many real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in simplifying expressions and apply these skills to solve problems in a variety of fields.

Tips and Tricks

• Practice, practice, practice! The more you practice simplifying expressions, the more comfortable you will become with these skills.
• Use a calculator to check your work when simplifying expressions.
• Break down complex expressions into smaller, more manageable parts.
• Use a diagram or chart to help you visualize the expression and identify like terms.

Real-World Applications

Combining like terms and simplifying expressions is an essential skill in algebra that has many real-world applications. For example:

• In physics, combining like terms and simplifying expressions is used to solve problems involving motion, energy, and momentum.
• In engineering, combining like terms and simplifying expressions is used to design and optimize systems, such as electrical circuits and mechanical systems.
• In economics, combining like terms and simplifying expressions is used to analyze and model economic systems, such as supply and demand curves.

Conclusion

In conclusion, performing algebraic operations, such as combining like terms and simplifying expressions, is an essential skill in algebra that has many real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in simplifying expressions and apply these skills to solve problems in a variety of fields.