Not applying mathematical properties

Oct 13, 2025 by thesweetdesigns.com 62 views

Understanding the Problem

In this article, we will focus on simplifying a given algebraic expression by combining like terms and applying mathematical properties. The expression we will be working with is $21h - 10h + 16 - 9 + 14h + 5$ . Our goal is to rewrite this expression in a simpler form by combining like terms and applying mathematical properties.

Step 1: Apply the Commutative Property

The commutative property states that the order of the terms in an expression does not change the value of the expression. We can use this property to rearrange the terms in the given expression.

21h - 10h + 16 - 9 + 14h + 5 = 21h - 10h + 14h + 16 - 9 + 5

Step 2: Combine Like Terms

Like terms are terms that have the same variable raised to the same power. In this case, we have three like terms: $21h$ , $-10h$ , and $14h$ . We can combine these terms by adding their coefficients.

21h - 10h + 14h = (21 - 10 + 14)h = 25h

Step 3: Simplify the Constant Terms

The constant terms in the expression are $16$ , $-9$ , and $5$ . We can simplify these terms by adding them together.

16 - 9 + 5 = 12

Step 4: Combine the Simplified Terms

Now that we have simplified the like terms and the constant terms, we can combine them to get the final simplified expression.

25h + 12

Conclusion

In this article, we have simplified the given algebraic expression by combining like terms and applying mathematical properties. We have shown that the expression $21h - 10h + 16 - 9 + 14h + 5$ is equivalent to $25h + 12$ . This simplified expression is easier to work with and can be used in a variety of mathematical applications.

Final Answer

The final answer is $\boxed{25h + 12}$ .

Discussion

This problem is a great example of how to simplify algebraic expressions by combining like terms and applying mathematical properties. By following these steps, we can simplify complex expressions and make them easier to work with. This is an important skill to have in mathematics, as it allows us to solve problems more efficiently and effectively.

Real-World Applications

Simplifying algebraic expressions is an important skill in a variety of real-world applications, including:

Science: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of populations.
Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Common Mistakes

When simplifying algebraic expressions, there are several common mistakes to avoid:

Not combining like terms: Failing to combine like terms can lead to a more complex expression than necessary.
Not applying mathematical properties: Failing to apply mathematical properties, such as the commutative property, can lead to a more complex expression than necessary.
Not checking for errors: Failing to check for errors can lead to incorrect solutions.

Tips and Tricks

Here are some tips and tricks for simplifying algebraic expressions:

Use the commutative property: The commutative property can be used to rearrange terms in an expression and make it easier to combine like terms.
Combine like terms first: Combining like terms first can make it easier to simplify the expression.
Check for errors: Checking for errors can help ensure that the solution is correct.

Conclusion

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants.

Q: What is the commutative property?

A: The commutative property is a mathematical property that states that the order of the terms in an expression does not change the value of the expression. For example, $a + b = b + a$ .

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable raised to the same power. Then, you can add or subtract the coefficients of these terms. For example, $2x + 3x = (2 + 3)x = 5x$ .

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

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

Not combining like terms
Not applying mathematical properties, such as the commutative property
Not checking for errors

Q: How do I check for errors when simplifying algebraic expressions?

A: To check for errors when simplifying algebraic expressions, you can:

Plug in values for the variables and check if the expression is true
Use a calculator to check if the expression is true
Check if the expression is equivalent to the original expression

Q: What are some tips and tricks for simplifying algebraic expressions?

A: Some tips and tricks for simplifying algebraic expressions include:

Using the commutative property to rearrange terms
Combining like terms first
Checking for errors

Q: How do I apply the distributive property when simplifying algebraic expressions?

A: The distributive property states that $a(b + c) = ab + ac$ . To apply the distributive property when simplifying algebraic expressions, you can:

Multiply the terms inside the parentheses by the term outside the parentheses
Simplify the resulting expression

Q: What is the difference between an algebraic expression and an equation?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. An equation is a statement that says two expressions are equal. For example, $2x + 3 = 5$ is an equation, while $2x + 3$ is an algebraic expression.

Q: How do I solve an equation that involves an algebraic expression?

A: To solve an equation that involves an algebraic expression, you can:

Simplify the algebraic expression
Isolate the variable
Solve for the variable

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

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

Science: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of populations.
Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, simplifying algebraic expressions is an important skill in mathematics that can be used in a variety of real-world applications. By following the steps outlined in this article, you can simplify complex expressions and make them easier to work with. Remember to avoid common mistakes and use tips and tricks to make the process easier.