Use A Horizontal Format To Simplify The Expression.$(-9x^2 + 9x + 6) + (6x^2 + X + 6$\]

Feb 26, 2025 by ADMIN 88 views

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

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Introduction

Algebraic expressions can be complex and difficult to understand, especially when they involve multiple terms and variables. However, with the right approach, we can simplify these expressions and make them more manageable. In this article, we will explore how to simplify the expression $(-9x^2 + 9x + 6) + (6x^2 + x + 6)$ using a horizontal format.

Understanding the Expression

The given expression is a combination of two algebraic expressions: $(-9x^2 + 9x + 6)$ and $(6x^2 + x + 6)$ . To simplify this expression, 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 simplifying the expression is to identify like terms. We can do this by looking at the terms in each expression and identifying the terms that have the same variable and exponent.

In the first expression, we have $-9x^2$ , $9x$ , and $6$ .
In the second expression, we have $6x^2$ , $x$ , and $6$ .

Step 2: Combine Like Terms

Now that we have identified like terms, we can combine them. We can do this by adding or subtracting the coefficients of the like terms.

The term $-9x^2$ in the first expression has a coefficient of $-9$ , while the term $6x^2$ in the second expression has a coefficient of $6$ . Since these terms have the same variable and exponent, we can combine them by adding their coefficients: $-9x^2 + 6x^2 = -3x^2$ .
The term $9x$ in the first expression has a coefficient of $9$ , while the term $x$ in the second expression has a coefficient of $1$ . Since these terms have the same variable and exponent, we can combine them by adding their coefficients: $9x + x = 10x$ .
The term $6$ in the first expression has a coefficient of $6$ , while the term $6$ in the second expression has a coefficient of $6$ . Since these terms have the same variable and exponent, we can combine them by adding their coefficients: $6 + 6 = 12$ .

Step 3: Simplify the Expression

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

We have $-3x^2$ from the combination of the $-9x^2$ and $6x^2$ terms.
We have $10x$ from the combination of the $9x$ and $x$ terms.
We have $12$ from the combination of the $6$ and $6$ terms.

Conclusion

In this article, we have simplified the expression $(-9x^2 + 9x + 6) + (6x^2 + x + 6)$ using a horizontal format. We have identified like terms, combined them, and simplified the expression. The final simplified expression is $-3x^2 + 10x + 12$ .

Example Use Case

Simplifying algebraic expressions is an essential skill in mathematics, and it has many practical applications in real-life situations. For example, in physics, we often need to simplify complex expressions to describe the motion of objects. In economics, we need to simplify complex expressions to model the behavior of markets. In engineering, we need to simplify complex expressions to design and optimize systems.

Tips and Tricks

When simplifying algebraic expressions, it is essential to identify like terms and combine them.
When combining like terms, we need to add or subtract the coefficients of the like terms.
When simplifying expressions, we need to combine the remaining terms to get the final simplified expression.

Common Mistakes

One common mistake when simplifying algebraic expressions is to forget to combine like terms.
Another common mistake is to add or subtract the wrong coefficients of like terms.
A third common mistake is to forget to combine the remaining terms after combining like terms.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill in mathematics, and it has many practical applications in real-life situations. By identifying like terms, combining them, and simplifying the expression, we can simplify complex expressions and make them more manageable. With practice and patience, we can master the art of simplifying algebraic expressions and apply it to real-life situations.

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Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Q: What is the purpose of simplifying algebraic expressions?

A: The purpose of simplifying algebraic expressions is to make them more manageable and easier to work with. Simplifying expressions can help us to:

Identify patterns and relationships between variables
Solve equations and inequalities
Model real-world situations
Make predictions and forecasts

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

A: To identify like terms in an algebraic expression, you need to look for terms that have the same variable and exponent. For example, in the expression $2x^2 + 3x + 4$ , the terms $2x^2$ and $3x$ are like terms because they have the same variable ( $x$ ) and exponent ( $2$ ).

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

A: To combine like terms in an algebraic expression, you need to add or subtract the coefficients of the like terms. For example, in the expression $2x^2 + 3x + 4$ , the terms $2x^2$ and $3x$ are like terms. To combine them, you would add their coefficients: $2x^2 + 3x = (2+3)x^2 = 5x^2$ .

Q: What is the difference between a variable and a constant in an algebraic expression?

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

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

A: To simplify an algebraic expression with multiple variables, you need to identify like terms and combine them. For example, in the expression $2x^2 + 3y^2 + 4x + 5y$ , the terms $2x^2$ and $3y^2$ are like terms, as are the terms $4x$ and $5y$ . To simplify the expression, you would combine the like terms: $2x^2 + 3y^2 + 4x + 5y = (2+0)x^2 + (0+5)y^2 + (4+0)x + (0+5)y = 2x^2 + 5y^2 + 4x + 5y$ .

Q: Can I simplify an algebraic expression with negative coefficients?

A: Yes, you can simplify an algebraic expression with negative coefficients. To do this, you need to follow the same steps as simplifying an expression with positive coefficients. For example, in the expression $-2x^2 + 3x - 4$ , the terms $-2x^2$ and $3x$ are like terms. To simplify the expression, you would combine the like terms: $-2x^2 + 3x - 4 = (-2+0)x^2 + (0+3)x + (-4+0) = -2x^2 + 3x - 4$ .

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

A: To check your work when simplifying an algebraic expression, you need to:

Verify that you have identified all like terms
Verify that you have combined the like terms correctly
Verify that the simplified expression is equivalent to the original expression

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

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

Forgetting to combine like terms
Adding or subtracting the wrong coefficients of like terms
Forgetting to combine the remaining terms after combining like terms
Not verifying that the simplified expression is equivalent to the original expression