Simplify The Expression: { -9n + (-9) + (-9) + (-5n) + 1$}$

Mar 10, 2025 by ADMIN 60 views

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

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying the given expression: ${-9n + (-9) + (-9) + (-5n) + 1}$ . We will break down the expression into manageable parts, apply the rules of algebra, and arrive at the simplified form.

Understanding the Expression

The given expression is a combination of variables and constants. It consists of two terms with the variable n, and three constant terms. To simplify the expression, we need to combine like terms and apply the rules of algebra.

Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, we have two terms with the variable n: -9n and -5n. These two terms are like terms because they both have the variable n raised to the power of 1.

Combining Like Terms

To combine like terms, we add or subtract the coefficients of the like terms. In this case, we have:

-9n (coefficient: -9)
-5n (coefficient: -5)

We add the coefficients: -9 + (-5) = -14. Therefore, the combined term is -14n.

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by combining the constant terms. We have:

-9 (constant term)
-9 (constant term)
1 (constant term)

We add the constant terms: -9 + (-9) + 1 = -17. Therefore, the simplified expression is:

-14n - 17

Conclusion

In this article, we simplified the given expression by combining like terms and applying the rules of algebra. We arrived at the simplified form: -14n - 17. This example demonstrates the importance of simplifying algebraic expressions, which is a crucial skill for students and professionals in mathematics and related fields.

Tips and Tricks

When simplifying algebraic expressions, always look for like terms and combine them.
Apply the rules of algebra, such as the distributive property and the commutative property.
Use parentheses to group terms and make the expression easier to read.
Check your work by plugging in values or using a calculator to verify the simplified expression.

Common Mistakes

Failing to identify like terms and combine them.
Applying the wrong rules of algebra, such as the distributive property or the commutative property.
Not using parentheses to group terms and make the expression easier to read.
Not checking the work by plugging in values or using a calculator to verify the simplified expression.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in mathematics and related fields. Some examples include:

Physics: Simplifying algebraic expressions is essential in physics, where equations often involve variables and constants. By simplifying these expressions, physicists can solve problems and make predictions about the behavior of physical systems.
Engineering: Simplifying algebraic expressions is also crucial in engineering, where equations often involve variables and constants. By simplifying these expressions, engineers can design and optimize systems, such as bridges, buildings, and electronic circuits.
Computer Science: Simplifying algebraic expressions is also important in computer science, where algorithms often involve variables and constants. By simplifying these expressions, computer scientists can optimize algorithms and improve the performance of computer systems.

Final Thoughts

Introduction

In our previous article, we explored the concept of simplifying algebraic expressions and provided a step-by-step guide on how to simplify the expression: ${-9n + (-9) + (-9) + (-5n) + 1}$ . In this article, we will answer some frequently asked questions (FAQs) about simplifying algebraic expressions.

Q&A

Q: What are like terms in algebra?

A: Like terms are terms that have the same variable raised to the same power. For example, in the expression 2x + 3x, 2x and 3x 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, you add or subtract the coefficients of the like terms. For example, in the expression 2x + 3x, you add the coefficients: 2 + 3 = 5. Therefore, the combined term is 5x.

Q: What are the rules of algebra that I need to follow when simplifying expressions?

A: The rules of algebra that you need to follow when simplifying expressions include:

The distributive property: a(b + c) = ab + ac
The commutative property: a + b = b + a
The associative property: (a + b) + c = a + (b + c)
The order of operations: PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction)

Q: How do I simplify expressions with parentheses?

A: To simplify expressions with parentheses, you need to follow the order of operations. First, evaluate the expressions inside the parentheses. Then, simplify the expression by combining like terms and applying the rules of algebra.

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 and combine them.
Applying the wrong rules of algebra, such as the distributive property or the commutative property.
Not using parentheses to group terms and make the expression easier to read.
Not checking the work by plugging in values or using a calculator to verify the simplified expression.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, you can plug in values or use a calculator to verify the simplified expression. For example, if you simplify the expression 2x + 3x to 5x, you can plug in a value for x and check if the expression is true.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has numerous real-world applications in mathematics and related fields. Some examples include:

Physics: Simplifying algebraic expressions is essential in physics, where equations often involve variables and constants. By simplifying these expressions, physicists can solve problems and make predictions about the behavior of physical systems.
Engineering: Simplifying algebraic expressions is also crucial in engineering, where equations often involve variables and constants. By simplifying these expressions, engineers can design and optimize systems, such as bridges, buildings, and electronic circuits.
Computer Science: Simplifying algebraic expressions is also important in computer science, where algorithms often involve variables and constants. By simplifying these expressions, computer scientists can optimize algorithms and improve the performance of computer systems.