Expand And Simplify $4(6f - 5) + 8f$.

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of expanding and simplifying the algebraic expression $4(6f - 5) + 8f$. We will break down the expression into smaller parts, apply the distributive property, and combine like terms to arrive at the simplified form.

Understanding the Expression

The given expression is $4(6f - 5) + 8f$. To simplify this expression, we need to understand the order of operations and the properties of algebraic expressions. The expression consists of two parts: the first part is $4(6f - 5)$, and the second part is $8f$.

Expanding the Expression

To expand the 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 can apply this property to the first part of the expression, $4(6f - 5)$.

4(6f - 5) = 4 \cdot 6f - 4 \cdot 5

Using the distributive property, we can rewrite the expression as:

4(6f - 5) = 24f - 20

Combining Like Terms

Now that we have expanded the first part of the expression, we can combine like terms. The expression now becomes:

24f - 20 + 8f

We can combine the like terms $24f$ and $8f$ by adding their coefficients:

24f + 8f = 32f

So, the expression now becomes:

32f - 20

Simplified Form

The simplified form of the expression $4(6f - 5) + 8f$ is $32f - 20$. This is the final answer.

Conclusion

In this article, we have explored the process of expanding and simplifying the algebraic expression $4(6f - 5) + 8f$. We applied the distributive property to expand the expression and combined like terms to arrive at the simplified form. This process is essential for any math enthusiast, and it will help you to simplify complex algebraic expressions with ease.

Tips and Tricks

• Always apply the distributive property when expanding expressions.
• Combine like terms by adding their coefficients.
• Simplify expressions by removing any unnecessary parentheses or brackets.

Practice Problems

Try simplifying the following expressions:

• $3(2x + 4) + 5x$
• $2(3y - 2) + 4y$
• $5(2z - 3) + 3z$

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example, in physics, you may need to simplify expressions to describe the motion of objects. In engineering, you may need to simplify expressions to design and optimize systems. In economics, you may need to simplify expressions to model and analyze economic systems.

Final Thoughts

Introduction

In our previous article, we explored the process of expanding and simplifying the algebraic expression $4(6f - 5) + 8f$. We applied the distributive property and combined like terms to arrive at the simplified form. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property allows us to expand expressions by multiplying each term inside the parentheses by the factor outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply each term inside the parentheses by the factor outside the parentheses. For example, if we have the expression $4(2x + 3)$, we can apply the distributive property by multiplying each term inside the parentheses by 4:

4(2x + 3) = 4 \cdot 2x + 4 \cdot 3

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. Like terms can be combined by adding their coefficients.

Q: How do I combine like terms?

A: To combine like terms, simply add their coefficients. For example, if we have the expression $2x + 5x$, we can combine the like terms by adding their coefficients:

2x + 5x = (2 + 5)x = 7x

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying expressions. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify expressions with multiple variables?

A: To simplify expressions with multiple variables, simply apply the distributive property and combine like terms. For example, if we have the expression $2x + 3y + 4x$, we can simplify it by combining the like terms:

2x + 3y + 4x = (2 + 4)x + 3y = 6x + 3y

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

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

• Forgetting to apply the distributive property
• Not combining like terms
• Not following the order of operations
• Making errors when multiplying or dividing

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By applying the distributive property and combining like terms, you can simplify complex expressions with ease. Remember to always practice and review the concepts to become proficient in simplifying algebraic expressions.