Simplify The Following Expression:$5(x+y) + 3(x-y$\]$\square$ $\square$ Y

$$

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms and removing any unnecessary components from the expression. In this article, we will simplify the given expression $5(x+y) + 3(x-y)$ using the distributive property and combining like terms.

Understanding the Expression

The given expression is a combination of two terms: $5(x+y)$ and $3(x-y)$. To simplify this expression, we need to understand the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We will use this property to expand the terms and then combine like terms.

Expanding the Terms

Using the distributive property, we can expand the first term $5(x+y)$ as follows:

$$5(x+y) = 5x + 5y$$

Similarly, we can expand the second term $3(x-y)$ as follows:

$$3(x-y) = 3x - 3y$$

Combining Like Terms

Now that we have expanded the terms, we can combine like terms to simplify the expression. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: $5x$ and $3x$, and two like terms: $5y$ and $-3y$.

We can combine the like terms as follows:

$$5x + 3x = 8x$$

$$5y - 3y = 2y$$

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by adding the two simplified terms:

$$8x + 2y$$

Conclusion

In this article, we simplified the expression $5(x+y) + 3(x-y)$ using the distributive property and combining like terms. We expanded the terms using the distributive property and then combined like terms to simplify the expression. The final simplified expression is $8x + 2y$.

Tips and Tricks

• When simplifying expressions, always look for like terms and combine them.
• Use the distributive property to expand terms and make it easier to combine like terms.
• Be careful when combining like terms, as the signs of the terms may change.

Real-World Applications

Simplifying expressions is an essential skill in algebra and is used in many real-world applications, such as:

• Physics: Simplifying expressions is used to solve equations and inequalities in physics, such as the equation of motion.
• Engineering: Simplifying expressions is used to solve equations and inequalities in engineering, such as the equation of a circuit.
• Computer Science: Simplifying expressions is used to solve equations and inequalities in computer science, such as the equation of a program.

Common Mistakes

• Not combining like terms: Failing to combine like terms can lead to incorrect solutions.
• Not using the distributive property: Failing to use the distributive property can make it difficult to combine like terms.
• Not being careful with signs: Failing to be careful with signs can lead to incorrect solutions.

Final Thoughts

Simplifying expressions is a crucial skill in algebra and is used in many real-world applications. By understanding the distributive property and combining like terms, we can simplify expressions and solve equations and inequalities. Remember to always look for like terms and combine them, use the distributive property to expand terms, and be careful with signs.

Additional Resources

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

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a rule that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$.
• Q: How do I combine like terms? A: To combine like terms, look for terms that have the same variable raised to the same power and add or subtract them.
• Q: What are some common mistakes to avoid when simplifying expressions? A: Some common mistakes to avoid when simplifying expressions include not combining like terms, not using the distributive property, and not being careful with signs.
  

$$

Introduction

In our previous article, we simplified the expression $5(x+y) + 3(x-y)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions about simplifying expressions and provide additional resources for further learning.

Q&A

Q: What is the distributive property?

A: The distributive property is a rule that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This means that we can distribute the value of $a$ to both $b$ and $c$ and then add the results.

Q: How do I combine like terms?

A: To combine like terms, look for terms that have the same variable raised to the same power and add or subtract them. For example, if we have the expression $2x + 3x$, we can combine the like terms by adding them together: $2x + 3x = 5x$.

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

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

• Not combining like terms
• Not using the distributive property
• Not being careful with signs
• Not checking for errors in the original expression

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms that can be combined. In other words, if we have an expression and we have combined all the like terms, then the expression is simplified.

Q: Can I simplify expressions with variables in the denominator?

A: Yes, we can simplify expressions with variables in the denominator. However, we need to be careful when simplifying expressions with variables in the denominator, as the signs of the terms may change.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses.
2. Exponents: Evaluate any exponents.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: Can I simplify expressions with absolute values?

A: Yes, we can simplify expressions with absolute values. However, we need to be careful when simplifying expressions with absolute values, as the signs of the terms may change.

Q: How do I simplify expressions with square roots?

A: To simplify expressions with square roots, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses.
2. Exponents: Evaluate any exponents.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions
• Algebra.com: Simplifying Expressions
• Purplemath: Simplifying Expressions

Conclusion

Simplifying expressions is an essential skill in algebra and is used in many real-world applications. By understanding the distributive property and combining like terms, we can simplify expressions and solve equations and inequalities. Remember to always look for like terms and combine them, use the distributive property to expand terms, and be careful with signs.

Final Thoughts

Simplifying expressions is a crucial skill in algebra and is used in many real-world applications. By understanding the distributive property and combining like terms, we can simplify expressions and solve equations and inequalities. Remember to always look for like terms and combine them, use the distributive property to expand terms, and be careful with signs.

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a rule that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$.
• Q: How do I combine like terms? A: To combine like terms, look for terms that have the same variable raised to the same power and add or subtract them.
• Q: What are some common mistakes to avoid when simplifying expressions? A: Some common mistakes to avoid when simplifying expressions include not combining like terms, not using the distributive property, and not being careful with signs.

Tips and Tricks

• Always look for like terms and combine them.
• Use the distributive property to expand terms and make it easier to combine like terms.
• Be careful with signs when combining like terms.
• Check for errors in the original expression before simplifying it.

Real-World Applications

Simplifying expressions is an essential skill in algebra and is used in many real-world applications, such as:

• Physics: Simplifying expressions is used to solve equations and inequalities in physics, such as the equation of motion.
• Engineering: Simplifying expressions is used to solve equations and inequalities in engineering, such as the equation of a circuit.
• Computer Science: Simplifying expressions is used to solve equations and inequalities in computer science, such as the equation of a program.

Common Mistakes

• Not combining like terms: Failing to combine like terms can lead to incorrect solutions.
• Not using the distributive property: Failing to use the distributive property can make it difficult to combine like terms.
• Not being careful with signs: Failing to be careful with signs can lead to incorrect solutions.

Final Thoughts

Simplifying expressions is a crucial skill in algebra and is used in many real-world applications. By understanding the distributive property and combining like terms, we can simplify expressions and solve equations and inequalities. Remember to always look for like terms and combine them, use the distributive property to expand terms, and be careful with signs.