Simplify The Expression: ${18x^2 - 9}$
Understanding the Expression
When simplifying an algebraic expression, we need to combine like terms and eliminate any unnecessary components. In this case, we are given the expression 18x^2 - 9, and our goal is to simplify it.
What are Like Terms?
Like terms are terms that have the same variable raised to the same power. In the expression 18x^2 - 9, the term 18x^2 is a like term because it has the same variable (x) raised to the same power (2). The term -9, however, is a constant term and does not have a variable.
Simplifying the Expression
To simplify the expression 18x^2 - 9, we need to combine the like term 18x^2 with the constant term -9. However, since the term -9 does not have a variable, we cannot combine it with the term 18x^2. Therefore, the simplified expression is still 18x^2 - 9.
Factoring Out a Common Factor
Although we cannot combine the like term 18x^2 with the constant term -9, we can factor out a common factor from the term 18x^2. The greatest common factor of 18 and x^2 is 18, so we can factor out 18 from the term 18x^2. This gives us:
18x^2 - 9 = 18(x^2) - 9
Simplifying the Expression Further
Now that we have factored out the common factor 18 from the term 18x^2, we can simplify the expression further. We can rewrite the expression as:
18(x^2) - 9 = 18x^2 - 9
However, we can simplify the expression further by factoring out a common factor from the constant term -9. The greatest common factor of -9 and 18 is 9, so we can factor out 9 from the constant term -9. This gives us:
18x^2 - 9 = 18x^2 - 9(1)
Simplifying the Expression Even Further
Now that we have factored out the common factor 9 from the constant term -9, we can simplify the expression even further. We can rewrite the expression as:
18x^2 - 9(1) = 18x^2 - 9
However, we can simplify the expression even further by combining the like term 18x^2 with the constant term -9. Since the term -9 does not have a variable, we cannot combine it with the term 18x^2. Therefore, the simplified expression is still 18x^2 - 9.
Conclusion
In conclusion, the expression 18x^2 - 9 cannot be simplified further because the term -9 does not have a variable. However, we can factor out a common factor from the term 18x^2, which gives us 18(x^2) - 9. We can also simplify the expression further by factoring out a common factor from the constant term -9, which gives us 18x^2 - 9(1).
Final Answer
The final answer is 18x^2 - 9.
Step-by-Step Solution
Here is the step-by-step solution to simplify the expression 18x^2 - 9:
- Factor out a common factor from the term 18x^2: 18(x^2) - 9
- Simplify the expression further by factoring out a common factor from the constant term -9: 18x^2 - 9(1)
- Combine the like term 18x^2 with the constant term -9: 18x^2 - 9
Common Mistakes
When simplifying an algebraic expression, it is easy to make mistakes. Here are some common mistakes to avoid:
- Not factoring out a common factor from the term 18x^2
- Not simplifying the expression further by factoring out a common factor from the constant term -9
- Combining the like term 18x^2 with the constant term -9 when it is not possible to do so.
Tips and Tricks
Here are some tips and tricks to help you simplify algebraic expressions:
- Always factor out a common factor from the term 18x^2
- Simplify the expression further by factoring out a common factor from the constant term -9
- Be careful when combining like terms, and make sure it is possible to do so.
Real-World Applications
Simplifying algebraic expressions has many real-world applications. Here are a few examples:
- In physics, simplifying algebraic expressions is used to solve problems involving motion and energy.
- In engineering, simplifying algebraic expressions is used to design and optimize systems.
- In economics, simplifying algebraic expressions is used to model and analyze economic systems.
Conclusion
In conclusion, simplifying algebraic expressions is an important skill that has many real-world applications. By following the steps outlined in this article, you can simplify algebraic expressions and solve problems involving motion, energy, and economics. Remember to always factor out a common factor from the term 18x^2, simplify the expression further by factoring out a common factor from the constant term -9, and be careful when combining like terms.
Understanding the Expression
When simplifying an algebraic expression, we need to combine like terms and eliminate any unnecessary components. In this case, we are given the expression 18x^2 - 9, and our goal is to simplify it.
Q&A
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. In the expression 18x^2 - 9, the term 18x^2 is a like term because it has the same variable (x) raised to the same power (2).
Q: Can I combine the like term 18x^2 with the constant term -9?
A: No, you cannot combine the like term 18x^2 with the constant term -9. The term -9 does not have a variable, so it cannot be combined with the term 18x^2.
Q: How can I simplify the expression 18x^2 - 9?
A: You can simplify the expression 18x^2 - 9 by factoring out a common factor from the term 18x^2. This gives you 18(x^2) - 9.
Q: Can I simplify the expression further by factoring out a common factor from the constant term -9?
A: Yes, you can simplify the expression further by factoring out a common factor from the constant term -9. This gives you 18x^2 - 9(1).
Q: What is the final answer to the expression 18x^2 - 9?
A: The final answer to the expression 18x^2 - 9 is still 18x^2 - 9.
Q: What are some common mistakes to avoid when simplifying algebraic expressions?
A: Some common mistakes to avoid when simplifying algebraic expressions include:
- Not factoring out a common factor from the term 18x^2
- Not simplifying the expression further by factoring out a common factor from the constant term -9
- Combining the like term 18x^2 with the constant term -9 when it is not possible to do so.
Q: What are some tips and tricks to help me simplify algebraic expressions?
A: Some tips and tricks to help you simplify algebraic expressions include:
- Always factor out a common factor from the term 18x^2
- Simplify the expression further by factoring out a common factor from the constant term -9
- Be careful when combining like terms, and make sure it is possible to do so.
Q: How can I apply simplifying algebraic expressions to real-world problems?
A: Simplifying algebraic expressions has many real-world applications. Here are a few examples:
- In physics, simplifying algebraic expressions is used to solve problems involving motion and energy.
- In engineering, simplifying algebraic expressions is used to design and optimize systems.
- In economics, simplifying algebraic expressions is used to model and analyze economic systems.
Conclusion
In conclusion, simplifying algebraic expressions is an important skill that has many real-world applications. By following the steps outlined in this article, you can simplify algebraic expressions and solve problems involving motion, energy, and economics. Remember to always factor out a common factor from the term 18x^2, simplify the expression further by factoring out a common factor from the constant term -9, and be careful when combining like terms.
Final Answer
The final answer to the expression 18x^2 - 9 is still 18x^2 - 9.
Step-by-Step Solution
Here is the step-by-step solution to simplify the expression 18x^2 - 9:
- Factor out a common factor from the term 18x^2: 18(x^2) - 9
- Simplify the expression further by factoring out a common factor from the constant term -9: 18x^2 - 9(1)
- Combine the like term 18x^2 with the constant term -9: 18x^2 - 9
Common Mistakes
When simplifying an algebraic expression, it is easy to make mistakes. Here are some common mistakes to avoid:
- Not factoring out a common factor from the term 18x^2
- Not simplifying the expression further by factoring out a common factor from the constant term -9
- Combining the like term 18x^2 with the constant term -9 when it is not possible to do so.
Tips and Tricks
Here are some tips and tricks to help you simplify algebraic expressions:
- Always factor out a common factor from the term 18x^2
- Simplify the expression further by factoring out a common factor from the constant term -9
- Be careful when combining like terms, and make sure it is possible to do so.
Real-World Applications
Simplifying algebraic expressions has many real-world applications. Here are a few examples:
- In physics, simplifying algebraic expressions is used to solve problems involving motion and energy.
- In engineering, simplifying algebraic expressions is used to design and optimize systems.
- In economics, simplifying algebraic expressions is used to model and analyze economic systems.