Simplify 5 ( 6 − O B ) + 2 ( 7 + 3 A B 5(6 - Ob) + 2(7 + 3ab 5 ( 6 − O B ) + 2 ( 7 + 3 Ab ].

$$

Introduction to Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill for students to master. In this article, we will focus on simplifying a specific algebraic expression: $5(6 - ob) + 2(7 + 3ab)$. This expression involves variables, constants, and mathematical operations, making it a great example for demonstrating the steps involved in simplifying algebraic expressions.

Understanding the Expression

Before we dive into simplifying the expression, let's break it down and understand what it represents. The expression consists of two terms: $5(6 - ob)$ and $2(7 + 3ab)$. Each term is a product of a constant and a binomial expression. The binomial expressions are $6 - ob$ and $7 + 3ab$, respectively.

Distributive Property

To simplify the expression, we will use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We will apply this property to each term in the expression.

Distributing the Constants

Let's start by distributing the constants in the first term: $5(6 - ob)$. Using the distributive property, we can rewrite this term as:

$5(6 - ob) = 5 \cdot 6 - 5 \cdot ob$

This simplifies to:

$30 - 5ob$

Distributing the Constants in the Second Term

Now, let's distribute the constants in the second term: $2(7 + 3ab)$. Using the distributive property, we can rewrite this term as:

$2(7 + 3ab) = 2 \cdot 7 + 2 \cdot 3ab$

This simplifies to:

$14 + 6ab$

Combining Like Terms

Now that we have distributed the constants, we can combine like terms. The expression now looks like this:

$30 - 5ob + 14 + 6ab$

We can combine the constant terms by adding them together:

$30 + 14 = 44$

So, the expression now looks like this:

$44 - 5ob + 6ab$

Final Simplification

The final step is to combine the like terms involving the variables. We can do this by combining the terms with the variable $b$ and the terms with the variable $a$.

$-5ob + 6ab = (6a - 5b)b$

However, this is not the correct simplification. We can simplify the expression by combining the like terms as follows:

$44 - 5ob + 6ab = 44 + 6ab - 5ob$

This simplifies to:

$44 + 6ab - 5ob$

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$$

Introduction

In our previous article, we explored the process of simplifying the algebraic expression $5(6 - ob) + 2(7 + 3ab)$. We used the distributive property to distribute the constants and then combined like terms. However, we encountered some difficulties in simplifying the expression. In this Q&A article, we will address some common questions and provide additional insights to help you better understand the process of simplifying algebraic expressions.

Q: What is the distributive property, and how is it used in simplifying algebraic expressions?

A: The distributive property is a fundamental concept in algebra that allows us to distribute a constant to each term inside a binomial expression. In the expression $5(6 - ob)$, we can use the distributive property to rewrite it as $5 \cdot 6 - 5 \cdot ob$. This simplifies to $30 - 5ob$.

Q: How do I know which terms to combine when simplifying an algebraic expression?

A: When simplifying an algebraic expression, you should combine like terms. Like terms are terms that have the same variable raised to the same power. In the expression $44 + 6ab - 5ob$, we can combine the like terms $6ab$ and $-5ob$ by adding their coefficients.

Q: What is the difference between combining like terms and simplifying an algebraic expression?

A: Combining like terms is a step in simplifying an algebraic expression. When you combine like terms, you are essentially adding or subtracting the coefficients of the terms with the same variable raised to the same power. Simplifying an algebraic expression involves using various techniques, such as the distributive property, to rewrite the expression in a simpler form.

Q: How do I know when to use the distributive property and when to combine like terms?

A: The distributive property is used when you have a constant multiplied by a binomial expression. In this case, you can use the distributive property to rewrite the expression and then combine like terms. On the other hand, when you have an expression with multiple terms, you should combine like terms to simplify the expression.

Q: Can you provide an example of a more complex algebraic expression that requires simplification?

A: Consider the expression $3(2x + 5) - 2(3x - 4)$. To simplify this expression, we can use the distributive property to rewrite it as $6x + 15 - 6x + 8$. We can then combine like terms to get $23$.

Q: How do I know if I have simplified an algebraic expression correctly?

A: To check if you have simplified an algebraic expression correctly, you can plug in values for the variables and evaluate the expression. If the expression simplifies to the same value for different values of the variables, then you have simplified it correctly.

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

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

• Not using the distributive property when necessary
• Not combining like terms
• Not checking if the expression has been simplified correctly
• Not using the correct order of operations

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of the distributive property and like terms. By following the steps outlined in this Q&A article, you can simplify algebraic expressions with confidence. Remember to use the distributive property when necessary, combine like terms, and check if the expression has been simplified correctly. With practice and patience, you will become proficient in simplifying algebraic expressions and solving complex mathematical problems.