Simplify The Following Expression:$ -3x^2 + 2 + 13x^2 - 9x $

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms, removing unnecessary components, and rearranging the expression to make it more manageable. In this article, we will simplify the given expression: $-3x^2 + 2 + 13x^2 - 9x$. We will break down the process into manageable steps, making it easy to follow and understand.

Understanding the Expression

Before we start simplifying the expression, let's take a closer look at what we're dealing with. The given expression is:

$-3x^2 + 2 + 13x^2 - 9x$

This expression consists of three terms:

1. $-3x^2$
2. $2$
3. $13x^2 - 9x$

Step 1: Combine Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, we have two like terms: $-3x^2$ and $13x^2$. We can combine these two terms by adding their coefficients.

$-3x^2 + 13x^2 = (13 - 3)x^2 = 10x^2$

So, the expression now becomes:

$10x^2 + 2 - 9x$

Step 2: Rearrange the Expression

Now that we have combined the like terms, let's rearrange the expression to make it more manageable. We can group the terms with the same variable together.

$10x^2 - 9x + 2$

Step 3: Final Simplification

The expression is now simplified, but we can take it a step further by rearranging the terms in descending order of the variable's exponent.

$10x^2 - 9x + 2$

This is the final simplified expression.

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and inequalities. By combining like terms and rearranging the expression, we can make it more manageable and easier to work with. In this article, we simplified the expression $-3x^2 + 2 + 13x^2 - 9x$ by combining like terms and rearranging the expression. We hope this article has helped you understand the process of simplifying expressions and how to apply it to your own algebraic manipulations.

Common Mistakes to Avoid

When simplifying expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not combining like terms: Make sure to combine like terms to simplify the expression.
• Not rearranging the expression: Rearrange the expression to make it more manageable and easier to work with.
• Not checking for errors: Double-check your work to ensure that the expression is simplified correctly.

Real-World Applications

Simplifying expressions has many real-world applications. Here are a few examples:

• Physics: Simplifying expressions is crucial in physics, where equations often involve complex variables and constants.
• Engineering: Engineers use algebraic manipulations to solve problems in fields like mechanics, thermodynamics, and electrical engineering.
• Computer Science: Simplifying expressions is essential in computer science, where algorithms often involve complex mathematical operations.

Final Thoughts

Introduction

In our previous article, we simplified the expression $-3x^2 + 2 + 13x^2 - 9x$ by combining like terms and rearranging the expression. In this article, we will answer some frequently asked questions about simplifying expressions and provide additional guidance on how to apply algebraic manipulation in real-world scenarios.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms. For example, $2x + 5x = (2 + 5)x = 7x$.

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. For example, $x$ is a variable. A constant is a value that does not change. For example, 2 is a constant.

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

A: To simplify an expression with multiple variables, combine like terms and rearrange the expression to make it more manageable. For example, $2x^2 + 3y^2 + 4x^2 + 5y^2 = (2 + 4)x^2 + (3 + 5)y^2 = 6x^2 + 8y^2$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying 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 with fractions?

A: To simplify an expression with fractions, multiply the numerator and denominator by the same value to eliminate the fraction. For example, $\frac{2x}{3} = \frac{2x \cdot 3}{3 \cdot 3} = \frac{6x}{9}$.

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression with a variable raised to the power of 1. For example, $2x + 3$ is a linear expression. A quadratic expression is an expression with a variable raised to the power of 2. For example, $x^2 + 2x + 3$ is a quadratic expression.

Q: How do I simplify an expression with absolute values?

A: To simplify an expression with absolute values, evaluate the expression inside the absolute value first. For example, $|2x + 3| = 2x + 3$ if $2x + 3 \geq 0$, and $-(2x + 3) = -2x - 3$ if $2x + 3 < 0$.

Real-World Applications

Simplifying expressions has many real-world applications. Here are a few examples:

• Physics: Simplifying expressions is crucial in physics, where equations often involve complex variables and constants.
• Engineering: Engineers use algebraic manipulations to solve problems in fields like mechanics, thermodynamics, and electrical engineering.
• Computer Science: Simplifying expressions is essential in computer science, where algorithms often involve complex mathematical operations.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that helps us solve equations and inequalities. By combining like terms and rearranging the expression, we can make it more manageable and easier to work with. We hope this article has helped you understand the process of simplifying expressions and how to apply it to your own algebraic manipulations. Remember to avoid common mistakes and check your work carefully to ensure that the expression is simplified correctly.