Write The Expanded Form Of The Expression.$a(8 + 2b - 6) = \square$

Introduction

In algebra, expressions are a combination of variables, constants, and mathematical operations. When we are given an expression in the form of $a(8 + 2b - 6) = \square$, our goal is to expand it and simplify it to a more manageable form. In this article, we will explore the process of expanding the given expression and provide a step-by-step guide on how to do it.

Understanding the Expression

The given expression is $a(8 + 2b - 6) = \square$. To expand this expression, we need to apply the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. In this case, we have $a(8 + 2b - 6)$, and we want to expand it.

Applying the Distributive Property

To apply the distributive property, we need to multiply the term $a$ with each term inside the parentheses. This means we will multiply $a$ with $8$, $2b$, and $-6$ separately.

Multiplying $a$ with $8$

When we multiply $a$ with $8$, we get $8a$.

Multiplying $a$ with $2b$

When we multiply $a$ with $2b$, we get $2ab$.

Multiplying $a$ with $-6$

When we multiply $a$ with $-6$, we get $-6a$.

Combining the Terms

Now that we have multiplied $a$ with each term inside the parentheses, we can combine the terms to get the expanded form of the expression.

$a(8 + 2b - 6) = 8a + 2ab - 6a$

Simplifying the Expression

We can simplify the expression further by combining like terms. In this case, we have $8a$ and $-6a$, which are like terms. We can combine them by adding their coefficients.

$8a - 6a = 2a$

So, the simplified form of the expression is $2a + 2ab$.

Conclusion

In this article, we expanded the given expression $a(8 + 2b - 6) = \square$ using the distributive property. We applied the distributive property to multiply the term $a$ with each term inside the parentheses and then combined the terms to get the expanded form of the expression. Finally, we simplified the expression by combining like terms.

Step-by-Step Guide

Here is a step-by-step guide on how to expand the given expression:

1. Identify the terms inside the parentheses.
2. Multiply the term $a$ with each term inside the parentheses.
3. Combine the terms to get the expanded form of the expression.
4. Simplify the expression by combining like terms.

Example

Let's consider an example to illustrate the process of expanding the expression.

Suppose we have the expression $a(3x + 2y - 4) = \square$. To expand this expression, we can follow the same steps as before.

1. Identify the terms inside the parentheses: $3x$, $2y$, and $-4$.
2. Multiply the term $a$ with each term inside the parentheses: $3ax$, $2ay$, and $-4a$.
3. Combine the terms to get the expanded form of the expression: $3ax + 2ay - 4a$.
4. Simplify the expression by combining like terms: $3ax + 2ay - 4a$.

Common Mistakes

When expanding expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not applying the distributive property correctly.
• Not combining like terms correctly.
• Not simplifying the expression correctly.

Tips and Tricks

Here are some tips and tricks to help you expand expressions correctly:

• Make sure to apply the distributive property correctly.
• Combine like terms carefully.
• Simplify the expression by combining like terms.
• Check your work by plugging in values for the variables.

Conclusion

In this article, we expanded the given expression $a(8 + 2b - 6) = \square$ using the distributive property. We applied the distributive property to multiply the term $a$ with each term inside the parentheses and then combined the terms to get the expanded form of the expression. Finally, we simplified the expression by combining like terms. We also provided a step-by-step guide on how to expand the expression and discussed common mistakes to avoid.

Introduction

In our previous article, we expanded the given expression $a(8 + 2b - 6) = \square$ using the distributive property. We applied the distributive property to multiply the term $a$ with each term inside the parentheses and then combined the terms to get the expanded form of the expression. In this article, we will answer some frequently asked questions about expanding expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical concept 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, you need to multiply the term by each term inside the parentheses. For example, if we have the expression $a(3x + 2y - 4)$, we would multiply $a$ with $3x$, $2y$, and $-4$ separately.

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property and the commutative property are two different mathematical concepts. The distributive property states that we can multiply a single term by each term inside the parentheses, while the commutative property states that the order of the terms does not change the result.

Q: How do I simplify an expression after expanding it?

A: To simplify an expression after expanding it, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, if we have the expression $3x + 2x$, we can combine the terms to get $5x$.

Q: What is the importance of expanding expressions?

A: Expanding expressions is an important skill in algebra because it allows us to simplify complex expressions and solve equations. By expanding expressions, we can identify the variables and constants in the expression and perform operations on them.

Q: How do I know when to expand an expression?

A: You should expand an expression when you need to simplify it or when you need to perform operations on the variables and constants in the expression. For example, if you have the expression $a(3x + 2y - 4)$ and you need to multiply it by $2$, you would expand the expression first.

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

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

• Not applying the distributive property correctly
• Not combining like terms correctly
• Not simplifying the expression correctly

Q: How can I practice expanding expressions?

A: You can practice expanding expressions by working through examples and exercises. You can also use online resources and practice tests to help you improve your skills.

Conclusion

In this article, we answered some frequently asked questions about expanding expressions. We discussed the distributive property, how to apply it, and how to simplify expressions after expanding them. We also talked about the importance of expanding expressions and how to know when to expand an expression. Finally, we discussed some common mistakes to avoid and how to practice expanding expressions.

Tips and Tricks

Here are some tips and tricks to help you expand expressions correctly:

• Make sure to apply the distributive property correctly.
• Combine like terms carefully.
• Simplify the expression by combining like terms.
• Check your work by plugging in values for the variables.
• Practice, practice, practice!

Common Mistakes

Here are some common mistakes to avoid when expanding expressions:

• Not applying the distributive property correctly
• Not combining like terms correctly
• Not simplifying the expression correctly

Conclusion

Expanding expressions is an important skill in algebra that allows us to simplify complex expressions and solve equations. By understanding the distributive property and how to apply it, we can expand expressions correctly and simplify them to their simplest form. We hope that this article has helped you to understand the concept of expanding expressions and how to apply it in different situations.