Mathematical Properties and Rules

Oct 13, 2025 by miodeya.com 24 views

Introduction

In mathematics, simplifying expressions is a crucial step in solving equations and inequalities. The expression $$2(3+u)+7u$$ is a complex expression that requires several steps to simplify. In this article, we will analyze each step of the simplification process and provide the reason that justifies it.

Step 1: Distributive Property

The first step in simplifying the expression is to apply the distributive property. This property states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

Using this property, we can rewrite the expression as:

2(3+u) = 6 + 2u

The reason for this step is to apply the distributive property, which allows us to multiply the term 2 by each term inside the parentheses.

Step 2: Combine Like Terms

The next step is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable u:

6 + 2u + 7u

We can combine these two terms by adding their coefficients:

6 + 9u

The reason for this step is to combine like terms, which simplifies the expression and makes it easier to work with.

Step 3: Final Simplification

The final step is to simplify the expression by combining the constant term with the variable term:

6 + 9u

This is the final simplified form of the expression.

Conclusion

In conclusion, the expression $$2(3+u)+7u$$ is simplified in several steps. Each step is justified by the application of mathematical properties and rules. The distributive property is used to rewrite the expression, and like terms are combined to simplify the expression further. The final simplified form of the expression is $$6 + 9u$$.

Discussion

The expression simplification process is an essential skill in mathematics, and it requires a deep understanding of mathematical properties and rules. By applying these properties and rules, we can simplify complex expressions and make them easier to work with.

Reasons for Each Step

Step	Reason
1	Distributive property
2	Combine like terms
3	Final simplification

Mathematical Properties and Rules

The expression simplification process relies on several mathematical properties and rules, including:

Distributive property: a(b + c) = ab + ac
Like terms: terms with the same variable raised to the same power
Combining like terms: adding the coefficients of like terms

Real-World Applications

The expression simplification process has several real-world applications, including:

Algebra: simplifying expressions is a crucial step in solving equations and inequalities.
Calculus: simplifying expressions is necessary for finding derivatives and integrals.
Computer Science: simplifying expressions is used in computer programming and algorithm design.

Conclusion

Introduction

In our previous article, we analyzed the expression simplification process for the expression $$2(3+u)+7u$$. In this article, we will answer some frequently asked questions about the expression simplification process.

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

This property allows us to multiply a term by each term inside the parentheses.

Q: Why do we need to combine like terms?

A: We need to combine like terms to simplify the expression and make it easier to work with. Like terms are terms that have the same variable raised to the same power. By combining like terms, we can add their coefficients and simplify the expression.

Q: What is the final simplified form of the expression?

A: The final simplified form of the expression is $$6 + 9u$$.

Q: How do we apply the distributive property to the expression?

A: To apply the distributive property, we multiply the term 2 by each term inside the parentheses:

2(3+u) = 6 + 2u

Q: What are some real-world applications of the expression simplification process?

A: The expression simplification process has several real-world applications, including:

Algebra: simplifying expressions is a crucial step in solving equations and inequalities.
Calculus: simplifying expressions is necessary for finding derivatives and integrals.
Computer Science: simplifying expressions is used in computer programming and algorithm design.

Q: Why is it important to understand the expression simplification process?

A: Understanding the expression simplification process is essential for solving equations and inequalities, finding derivatives and integrals, and designing algorithms. It requires a deep understanding of mathematical properties and rules.

Q: Can you provide some examples of expressions that can be simplified using the distributive property?

A: Here are some examples of expressions that can be simplified using the distributive property:

$3(2x + 5) = 6x + 15$
$4(3y - 2) = 12y - 8$
$2(5z + 1) = 10z + 2$

Q: Can you provide some examples of expressions that can be simplified by combining like terms?

A: Here are some examples of expressions that can be simplified by combining like terms:

$2x + 3x = 5x$
$4y - 2y = 2y$
$3z + 2z = 5z$

Conclusion

In conclusion, the expression simplification process is an essential skill in mathematics that requires a deep understanding of mathematical properties and rules. By applying the distributive property and combining like terms, we can simplify complex expressions and make them easier to work with. We hope this Q&A article has provided you with a better understanding of the expression simplification process.

Frequently Asked Questions

Question	Answer
What is the distributive property?	The distributive property is a mathematical property that states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac
Why do we need to combine like terms?	We need to combine like terms to simplify the expression and make it easier to work with.
What is the final simplified form of the expression?	The final simplified form of the expression is $$6 + 9u$$
How do we apply the distributive property to the expression?	To apply the distributive property, we multiply the term 2 by each term inside the parentheses: $$2(3+u) = 6 + 2u$$
What are some real-world applications of the expression simplification process?	The expression simplification process has several real-world applications, including algebra, calculus, and computer science.

Mathematical Properties and Rules

The expression simplification process relies on several mathematical properties and rules, including:

Distributive property: a(b + c) = ab + ac
Like terms: terms with the same variable raised to the same power
Combining like terms: adding the coefficients of like terms

Real-World Applications

The expression simplification process has several real-world applications, including:

Algebra: simplifying expressions is a crucial step in solving equations and inequalities.
Calculus: simplifying expressions is necessary for finding derivatives and integrals.
Computer Science: simplifying expressions is used in computer programming and algorithm design.