Simplify The Expression: $\[ 4(5x - 1) - 8x + 11 \\]

Feb 28, 2025 by ADMIN 53 views

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the given expression: 4(5x - 1) - 8x + 11. We will use the distributive property, combine like terms, and apply other algebraic rules to simplify the expression.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions with parentheses. It states that for any numbers a, b, and c:

a(b + c) = ab + ac

This property can be applied to expressions with multiple terms inside the parentheses. In the given expression, we have 4(5x - 1), which can be expanded using the distributive property.

Expanding the Expression

Using the distributive property, we can expand the expression 4(5x - 1) as follows:

4(5x - 1) = 4(5x) - 4(1) = 20x - 4

Now, we can rewrite the original expression as:

20x - 4 - 8x + 11

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In the expression 20x - 4 - 8x + 11, we have two like terms: 20x and -8x. We can combine these terms by adding their coefficients.

20x - 8x = 12x

So, the expression becomes:

12x - 4 + 11

Simplifying the Expression

Now, we can simplify the expression by combining the constant terms. We have -4 and +11, which can be combined as follows:

-4 + 11 = 7

So, the simplified expression is:

12x + 7

Conclusion

In this article, we simplified the expression 4(5x - 1) - 8x + 11 using the distributive property and combining like terms. We expanded the expression using the distributive property, combined like terms, and simplified the expression by combining constant terms. The final simplified expression is 12x + 7.

Tips and Tricks

When simplifying expressions, always look for like terms and combine them.
Use the distributive property to expand expressions with parentheses.
Combine constant terms by adding or subtracting them.
Check your work by plugging in values for the variables and simplifying the expression.

Common Mistakes

Failing to combine like terms.
Not using the distributive property to expand expressions with parentheses.
Not combining constant terms.
Not checking your work by plugging in values for the variables.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, including:

Solving systems of equations.
Finding the maximum or minimum value of a function.
Modeling real-world situations using algebraic expressions.
Simplifying complex expressions in physics and engineering.

Final Thoughts

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By following the steps outlined in this article, you can simplify expressions like 4(5x - 1) - 8x + 11 and apply algebraic rules to solve real-world problems.

Introduction

In our previous article, we simplified the expression 4(5x - 1) - 8x + 11 using the distributive property and combining like terms. We expanded the expression, combined like terms, and simplified the expression by combining constant terms. 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 allows us to expand expressions with parentheses. It states that for any numbers a, b, and c:

a(b + c) = ab + ac

This property can be applied to expressions with multiple terms inside the parentheses.

Q: How do I expand an expression using the distributive property?

A: To expand an expression using the distributive property, you need to multiply each term inside the parentheses by the number outside the parentheses. For example, to expand 4(5x - 1), you would multiply 4 by each term inside the parentheses:

4(5x - 1) = 4(5x) - 4(1) = 20x - 4

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.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, to combine 2x and 5x, you would add their coefficients:

2x + 5x = 7x

Q: What are constant terms?

A: Constant terms are terms that do not have any variables. For example, 4 and 11 are constant terms because they do not have any variables.

Q: How do I combine constant terms?

A: To combine constant terms, you need to add or subtract them. For example, to combine -4 and 11, you would add them:

-4 + 11 = 7

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

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

Failing to combine like terms.
Not using the distributive property to expand expressions with parentheses.
Not combining constant terms.
Not checking your work by plugging in values for the variables.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

Solving systems of equations.
Finding the maximum or minimum value of a function.
Modeling real-world situations using algebraic expressions.
Simplifying complex expressions in physics and engineering.

Conclusion

In this article, we answered some frequently asked questions about simplifying algebraic expressions. We discussed the distributive property, like terms, combining like terms, constant terms, and combining constant terms. We also highlighted some common mistakes to avoid and real-world applications of simplifying algebraic expressions.

Tips and Tricks

Always use the distributive property to expand expressions with parentheses.
Combine like terms by adding or subtracting their coefficients.
Combine constant terms by adding or subtracting them.
Check your work by plugging in values for the variables.
Use algebraic rules to simplify complex expressions.