Simplify The Expression: { -5(n-1) - 3n$}$

$$

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the given expression: $-5(n-1) - 3n$. We will break down the expression step by step, using the distributive property and combining like terms to arrive at the simplified form.

Understanding the Expression

The given expression is $-5(n-1) - 3n$. To simplify this expression, we need to apply the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We will also use the commutative property, which states that for any real numbers $a$ and $b$, $a + b = b + a$.

Step 1: Apply the Distributive Property

The first step in simplifying the expression is to apply the distributive property to the term $-5(n-1)$. This means that we will multiply the $-5$ by each term inside the parentheses, $n$ and $-1$. Using the distributive property, we get:

$$-5(n-1) = -5n + 5$$

Step 2: Rewrite the Expression

Now that we have applied the distributive property, we can rewrite the original expression as:

$$-5(n-1) - 3n = (-5n + 5) - 3n$$

Step 3: Combine Like Terms

The next step is to combine like terms. In this case, we have two terms with the variable $n$, $-5n$ and $-3n$. We can combine these terms by adding their coefficients, which are $-5$ and $-3$. Using the commutative property, we can rewrite the expression as:

$$(-5n + 5) - 3n = -5n - 3n + 5$$

Step 4: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by adding the coefficients of the $n$ terms. Using the commutative property, we get:

$$-5n - 3n + 5 = -8n + 5$$

Conclusion

In conclusion, we have simplified the given expression $-5(n-1) - 3n$ by applying the distributive property and combining like terms. The simplified form of the expression is $-8n + 5$. This is the final answer to the problem.

Final Answer

The final answer to the problem is $-8n + 5$.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to apply the distributive property and combine like terms.
• Use the commutative property to rearrange terms and make it easier to combine like terms.
• Always check your work by plugging in values for the variables to ensure that the expression is simplified correctly.

Common Mistakes

• Failing to apply the distributive property when simplifying expressions with parentheses.
• Not combining like terms when simplifying expressions.
• Not checking work by plugging in values for the variables.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, including:

• Solving systems of equations in physics and engineering.
• Modeling population growth and decay in biology.
• Analyzing data in statistics and data science.

Further Reading

For further reading on simplifying algebraic expressions, we recommend the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By applying the distributive property and combining like terms, we can simplify expressions and arrive at the final answer. We hope that this article has provided a clear and concise explanation of how to simplify the expression $-5(n-1) - 3n$.

$$

Introduction

In our previous article, we simplified the expression $-5(n-1) - 3n$ by applying the distributive property and combining like terms. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a rule in algebra that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This means that we can multiply a single term by each term inside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the single term by each term inside the parentheses. For example, if we have the expression $-5(n-1)$, we would multiply the $-5$ by each term inside the parentheses, $n$ and $-1$, to get $-5n + 5$.

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, simply add or subtract the coefficients of the like terms. For example, if we have the expression $-5n + 3n$, we would combine the like terms by adding the coefficients, $-5$ and $3$, to get $-2n$.

Q: What is the commutative property?

A: The commutative property is a rule in algebra that states that for any real numbers $a$ and $b$, $a + b = b + a$. This means that we can rearrange the terms in an expression without changing its value.

Q: How do I use the commutative property?

A: To use the commutative property, simply rearrange the terms in the expression to make it easier to combine like terms. For example, if we have the expression $-5n - 3n$, we would rearrange the terms to get $-5n - 3n = -8n$.

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

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

• Failing to apply the distributive property when simplifying expressions with parentheses.
• Not combining like terms when simplifying expressions.
• Not checking work by plugging in values for the variables.

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

A: To check your work when simplifying algebraic expressions, simply plug in values for the variables and evaluate the expression. For example, if we have the expression $-5n + 5$ and we plug in $n = 2$, we get $-5(2) + 5 = -10 + 5 = -5$.

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

A: Some real-world applications of simplifying algebraic expressions include:

• Solving systems of equations in physics and engineering.
• Modeling population growth and decay in biology.
• Analyzing data in statistics and data science.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By applying the distributive property and combining like terms, we can simplify expressions and arrive at the final answer. We hope that this article has provided a clear and concise explanation of how to simplify the expression $-5(n-1) - 3n$ and has answered some frequently asked questions related to simplifying algebraic expressions.

Final Answer

The final answer to the problem is $-8n + 5$.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to apply the distributive property and combine like terms.
• Use the commutative property to rearrange terms and make it easier to combine like terms.
• Always check your work by plugging in values for the variables to ensure that the expression is simplified correctly.

Common Mistakes

• Failing to apply the distributive property when simplifying expressions with parentheses.
• Not combining like terms when simplifying expressions.
• Not checking work by plugging in values for the variables.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, including:

• Solving systems of equations in physics and engineering.
• Modeling population growth and decay in biology.
• Analyzing data in statistics and data science.

Further Reading

For further reading on simplifying algebraic expressions, we recommend the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions