Simplify The Expression:${ 5w + (-5w) - W + (-2w) }$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms and eliminating unnecessary components to arrive at a simpler form of the expression. In this article, we will focus on simplifying the given expression: $5w + (-5w) - w + (-2w)$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the process.

Understanding the Expression

The given expression is: $5w + (-5w) - w + (-2w)$. This expression consists of four terms, each containing a variable $w$ multiplied by a constant. The constants are $5$, $-5$, $-1$, and $-2$, respectively.

Step 1: Identify Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, we can identify two pairs of like terms:

• $5w$ and $-5w$
• $-w$ and $-2w$

These pairs of like terms can be combined to simplify the expression.

Step 2: Combine Like Terms

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

• $5w + (-5w) = 0$ (since the coefficients are opposites)
• $-w + (-2w) = -3w$ (since we add the coefficients)

So, the expression simplifies to: $0 - 3w$.

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression further. The expression $0 - 3w$ can be rewritten as $-3w$.

Conclusion

In this article, we simplified the given expression: $5w + (-5w) - w + (-2w)$. We identified like terms, combined them, and simplified the expression to arrive at the final answer: $-3w$. This process demonstrates the importance of simplifying expressions in mathematics and provides a clear understanding of the steps involved.

Tips and Tricks

• When simplifying expressions, always look for like terms and combine them.
• Use the distributive property to expand expressions and simplify them.
• Be careful when combining like terms, as the coefficients may be opposites or have different signs.

Common Mistakes to Avoid

• Failing to identify like terms and combine them.
• Not simplifying the expression further after combining like terms.
• Making errors when adding or subtracting coefficients.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has numerous real-world applications. In physics, for example, simplifying expressions helps us solve problems involving motion, energy, and momentum. In engineering, simplifying expressions is essential for designing and optimizing systems.

Practice Problems

1. Simplify the expression: $3x + (-3x) - 2x + (-4x)$.
2. Simplify the expression: $2y + (-2y) + 5y + (-3y)$.
3. Simplify the expression: $4z + (-4z) - 2z + (-6z)$.

Answer Key

1. $-7x$
2. $0$
3. $-10z$

Conclusion

Introduction

In our previous article, we simplified the expression: $5w + (-5w) - w + (-2w)$. We identified like terms, combined them, and simplified the expression to arrive at the final answer: $-3w$. In this article, we will provide a Q&A guide to help you understand the process of simplifying expressions.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In the expression $5w + (-5w) - w + (-2w)$, the terms $5w$ and $-5w$ are like terms because they both have the variable $w$ raised to the power of 1.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable raised to the same power. In the expression $5w + (-5w) - w + (-2w)$, we can identify two pairs of like terms:

• $5w$ and $-5w$
• $-w$ and $-2w$

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms. In the expression $5w + (-5w) - w + (-2w)$, we have:

• $5w + (-5w) = 0$ (since the coefficients are opposites)
• $-w + (-2w) = -3w$ (since we add the coefficients)

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to expand expressions by multiplying each term inside the parentheses by a constant. For example, in the expression $(3x + 2)(4)$, we can use the distributive property to expand it as: $3x(4) + 2(4) = 12x + 8$.

Q: How do I simplify expressions using the distributive property?

A: To simplify expressions using the distributive property, multiply each term inside the parentheses by a constant. For example, in the expression $(3x + 2)(4)$, we can use the distributive property to expand it as: $3x(4) + 2(4) = 12x + 8$.

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.
• Not simplifying the expression further after combining like terms.
• Making errors when adding or subtracting coefficients.

Q: How do I apply simplifying expressions in real-world scenarios?

A: Simplifying expressions is a crucial skill in mathematics that has numerous real-world applications. In physics, for example, simplifying expressions helps us solve problems involving motion, energy, and momentum. In engineering, simplifying expressions is essential for designing and optimizing systems.

Q: What are some practice problems to help me improve my skills in simplifying expressions?

A: Here are some practice problems to help you improve your skills in simplifying expressions:

1. Simplify the expression: $3x + (-3x) - 2x + (-4x)$.
2. Simplify the expression: $2y + (-2y) + 5y + (-3y)$.
3. Simplify the expression: $4z + (-4z) - 2z + (-6z)$.

Answer Key

1. $-7x$
2. $0$
3. $-10z$

Conclusion

Simplifying expressions is a fundamental concept in mathematics that helps us solve problems efficiently. By identifying like terms, combining them, and simplifying the expression, we can arrive at a simpler form of the expression. This process has numerous real-world applications and is essential for problem-solving in various fields.