Simplify The Expression:$4(1 - 2b) + 7b - 10$Type The Correct Answer In The Box.

Feb 26, 2025 by ADMIN 81 views

Introduction

In this article, we will simplify the given expression $4(1 - 2b) + 7b - 10$ . This involves using the distributive property, combining like terms, and rearranging the expression to its simplest form. We will also provide step-by-step solutions and explanations to help readers understand the process.

Step 1: Distribute the 4

The first step is to distribute the 4 to the terms inside the parentheses using the distributive property. This means multiplying the 4 by each term inside the parentheses.

4(1 - 2b) = 4(1) - 4(2b)

Using the distributive property, we get:

4(1 - 2b) = 4 - 8b

Step 2: Combine Like Terms

Now, we can combine the like terms in the expression. The like terms are the terms that have the same variable raised to the same power.

4 - 8b + 7b - 10

We can combine the like terms by adding or subtracting the coefficients of the same variable.

4 - 8b + 7b - 10 = 4 - 1b - 10

Step 3: Simplify the Expression

Now, we can simplify the expression by combining the constants and rearranging the terms.

4 - 1b - 10 = -6 - 1b

Conclusion

In this article, we simplified the expression $4(1 - 2b) + 7b - 10$ using the distributive property, combining like terms, and rearranging the expression to its simplest form. We provided step-by-step solutions and explanations to help readers understand the process.

Final Answer

The final answer is: $\boxed{-6 - 1b}$

Tips and Tricks

When simplifying expressions, always use the distributive property to distribute coefficients to terms inside parentheses.
Combine like terms by adding or subtracting the coefficients of the same variable.
Rearrange the terms to put the constants first and the variables last.

Common Mistakes

Failing to distribute coefficients to terms inside parentheses.
Not combining like terms.
Not rearranging the terms to put the constants first and the variables last.

Real-World Applications

Simplifying expressions is an essential skill in mathematics and has many real-world applications. For example, in physics, simplifying expressions is used to solve problems involving motion, energy, and momentum. In engineering, simplifying expressions is used to design and optimize systems, such as electrical circuits and mechanical systems.

Practice Problems

Try simplifying the following expressions:

$3(2x + 5) - 2x + 1$
$2(3y - 4) + 5y - 3$
$4(2z + 1) - 3z - 2$

Answer Key

$6x + 15 - 2x + 1 = 4x + 16$
$6y - 8 + 5y - 3 = 11y - 11$
$8z + 4 - 3z - 2 = 5z + 2$

References

[1] "Algebra" by Michael Artin
[2] "Calculus" by Michael Spivak
[3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
Simplify the Expression: $4(1 - 2b) + 7b - 10$ - Q&A =====================================================

Introduction

In our previous article, we simplified the expression $4(1 - 2b) + 7b - 10$ using the distributive property, combining like terms, and rearranging the expression to its simplest form. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that allows us to distribute a coefficient to the terms inside parentheses. For example, in the expression $4(1 - 2b)$ , we can distribute the 4 to the terms inside the parentheses using the distributive property.

Q: How do I combine like terms?

A: To combine like terms, we need to add or subtract the coefficients of the same variable. For example, in the expression $4 - 8b + 7b - 10$ , we can combine the like terms by adding or subtracting the coefficients of the variable b.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, in the expression $4 - 8b + 7b - 10$ , the terms $-8b$ and $7b$ are like terms because they both have the variable b raised to the power of 1.

Q: How do I simplify an expression?

A: To simplify an expression, we need to use the distributive property, combine like terms, and rearrange the expression to put the constants first and the variables last. For example, in the expression $4(1 - 2b) + 7b - 10$ , we can simplify it by distributing the 4, combining the like terms, and rearranging the expression.

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

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

Failing to distribute coefficients to terms inside parentheses.
Not combining like terms.
Not rearranging the terms to put the constants first and the variables last.

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

A: Simplifying expressions is an essential skill in mathematics and has many real-world applications. For example, in physics, simplifying expressions is used to solve problems involving motion, energy, and momentum. In engineering, simplifying expressions is used to design and optimize systems, such as electrical circuits and mechanical systems.

Q: What are some practice problems to try?

A: Here are some practice problems to try:

$3(2x + 5) - 2x + 1$
$2(3y - 4) + 5y - 3$
$4(2z + 1) - 3z - 2$

Answer Key

$6x + 15 - 2x + 1 = 4x + 16$
$6y - 8 + 5y - 3 = 11y - 11$
$8z + 4 - 3z - 2 = 5z + 2$

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to simplifying expressions. We covered topics such as the distributive property, combining like terms, and real-world applications of simplifying expressions. We also provided some practice problems to try.

Tips and Tricks

Always use the distributive property to distribute coefficients to terms inside parentheses.
Combine like terms by adding or subtracting the coefficients of the same variable.
Rearrange the terms to put the constants first and the variables last.