Simplify The Expression:$\[ 10x + 9 + 3 + 5x + 9x \\]
Introduction
In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms, removing unnecessary components, and rewriting the expression in a more manageable form. In this article, we will simplify the given expression: . We will break down the process into manageable steps, making it easy to understand and follow.
Understanding the Expression
The given expression is a combination of terms with variables and constants. To simplify it, we need to identify the like terms, which are the terms that have the same variable raised to the same power. In this case, the like terms are the terms with the variable .
Identifying Like Terms
The expression contains three terms with the variable : , , and . These terms are like terms because they all have the variable raised to the power of 1.
Combining Like Terms
To simplify the expression, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the like terms. In this case, we need to add the coefficients of the terms with the variable .
# Define the coefficients of the like terms
coefficient_1 = 10
coefficient_2 = 5
coefficient_3 = 9
# Add the coefficients
sum_of_coefficients = coefficient_1 + coefficient_2 + coefficient_3
print(sum_of_coefficients)
The output of the code is 24, which is the sum of the coefficients of the like terms.
Simplifying the Expression
Now that we have combined the like terms, we can simplify the expression by rewriting it in a more manageable form. We can do this by adding the constants and combining the like terms.
# Define the constants
constant_1 = 9
constant_2 = 3
# Add the constants
sum_of_constants = constant_1 + constant_2
# Simplify the expression
simplified_expression = f"{sum_of_coefficients}x + {sum_of_constants}"
print(simplified_expression)
The output of the code is 24x + 12, which is the simplified expression.
Conclusion
Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. By identifying like terms, combining them, and rewriting the expression in a more manageable form, we can simplify complex expressions. In this article, we simplified the expression by combining the like terms and adding the constants. We hope that this article has provided you with a clear understanding of how to simplify expressions and has helped you develop your problem-solving skills.
Final Answer
The final answer is .
Additional Resources
For more information on simplifying expressions, you can check out the following resources:
- Khan Academy: Simplifying Expressions
- Mathway: Simplifying Expressions
- Wolfram Alpha: Simplifying Expressions
FAQs
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power.
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract the coefficients of the like terms.
Q: What is the simplified expression?
Introduction
In our previous article, we simplified the expression by combining like terms and adding constants. In this article, we will provide a Q&A guide to help you understand the process of simplifying expressions.
Q&A Guide
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 , the terms and are like terms because they both have the variable raised to the power of 1.
Q: How do I identify like terms?
A: To identify like terms, you need to look for terms that have the same variable raised to the same power. You can do this by comparing the coefficients of the terms.
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, in the expression , you can combine the like terms and by adding their coefficients: . The resulting term is .
Q: What is the difference between combining like terms and adding constants?
A: Combining like terms involves adding or subtracting the coefficients of like terms, while adding constants involves adding or subtracting the constants in the expression.
Q: How do I add constants?
A: To add constants, you simply add or subtract the constants in the expression. For example, in the expression , you can add the constants and (since there is no constant term in the other terms) to get .
Q: What is the simplified expression?
A: The simplified expression is the expression that has been combined by adding or subtracting like terms and adding or subtracting constants.
Q: How do I check if an expression is simplified?
A: To check if an expression is simplified, you need to look for like terms and combine them. If there are no like terms left, then the expression is simplified.
Q: Can I simplify an expression with variables and constants?
A: Yes, you can simplify an expression with variables and constants by combining like terms and adding or subtracting constants.
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid when simplifying expressions include:
- Not identifying like terms
- Not combining like terms correctly
- Not adding or subtracting constants correctly
- Not checking if the expression is simplified
Conclusion
Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. By understanding the process of simplifying expressions and avoiding common mistakes, you can become proficient in simplifying expressions and solve problems with confidence.
Final Answer
The final answer is .
Additional Resources
For more information on simplifying expressions, you can check out the following resources:
- Khan Academy: Simplifying Expressions
- Mathway: Simplifying Expressions
- Wolfram Alpha: Simplifying Expressions
Practice Problems
Try simplifying the following expressions: