(2a²+3ab+7)-(3a²-11)
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Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of simplifying algebraic expressions, using the given expression (2a²+3ab+7)-(3a²-11) as an example.
Understanding Algebraic Expressions
An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It can be a simple expression, such as 2x, or a complex expression, such as 2x² + 3x - 4. Algebraic expressions can be combined using various mathematical operations, such as addition, subtraction, multiplication, and division.
Distributive Property
The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses by the term outside the parentheses. The distributive property can be written as:
a(b + c) = ab + ac
Simplifying the Given Expression
Now, let's apply the distributive property to simplify the given expression (2a²+3ab+7)-(3a²-11).
Step 1: Distribute the Negative Sign
When we subtract a term, we can distribute the negative sign to each term inside the parentheses. In this case, we have:
(2a²+3ab+7)-(3a²-11) = -3a² + 2a² + 3ab - 11 + 7
Step 2: Combine Like Terms
Now, let's combine like terms. Like terms are terms that have the same variable and exponent. In this case, we have:
-3a² + 2a² = -a² 3ab - 0 = 3ab -11 + 7 = -4
So, the simplified expression is:
-a² + 3ab - 4
Conclusion
Simplifying algebraic expressions is an essential skill for any math enthusiast. By applying the distributive property and combining like terms, we can simplify complex expressions and make them easier to work with. In this article, we used the given expression (2a²+3ab+7)-(3a²-11) as an example and simplified it step by step.
Tips and Tricks
Here are some tips and tricks to help you simplify algebraic expressions:
- Use the distributive property: The distributive property is a powerful tool for simplifying expressions. Make sure to apply it whenever possible.
- Combine like terms: Like terms are terms that have the same variable and exponent. Combine them to simplify the expression.
- Check your work: Always check your work to make sure that you have simplified the expression correctly.
Examples and Practice
Here are some examples and practice problems to help you practice simplifying algebraic expressions:
Example 1
Simplify the expression (2x² + 3x - 4) - (x² - 2x + 1)
Solution
(2x² + 3x - 4) - (x² - 2x + 1) = 2x² - x² + 3x + 2x - 4 - 1 = x² + 5x - 5
Example 2
Simplify the expression (3y² + 2y - 1) - (2y² - 3y + 2)
Solution
(3y² + 2y - 1) - (2y² - 3y + 2) = 3y² - 2y² + 2y + 3y - 1 - 2 = y² + 5y - 3
Final Thoughts
Simplifying algebraic expressions is an essential skill for any math enthusiast. By applying the distributive property and combining like terms, we can simplify complex expressions and make them easier to work with. Remember to use the distributive property, combine like terms, and check your work to ensure that you have simplified the expression correctly. With practice and patience, you will become a master of simplifying algebraic expressions in no time!
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Introduction
Simplifying algebraic expressions is a fundamental concept in mathematics, and it can be a challenging task for many students. In this article, we will address some of the most frequently asked questions about simplifying algebraic expressions.
Q&A
Q: What is the distributive property, and how is it used in simplifying algebraic expressions?
A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses by the term outside the parentheses. It is used to simplify algebraic expressions by distributing the negative sign to each term inside the parentheses.
Q: How do I combine like terms in an algebraic expression?
A: To combine like terms, you need to identify the terms that have the same variable and exponent. Then, you can add or subtract the coefficients of these terms to simplify the expression.
Q: What is the difference between a variable and a constant in an algebraic expression?
A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that does not change. In an algebraic expression, variables are often represented by letters such as x, y, or z, while constants are represented by numbers.
Q: How do I simplify an algebraic expression with multiple parentheses?
A: To simplify an algebraic expression with multiple parentheses, you need to apply the distributive property to each set of parentheses and then combine like terms.
Q: Can I simplify an algebraic expression with fractions?
A: Yes, you can simplify an algebraic expression with fractions by multiplying each term by the least common multiple (LCM) of the denominators.
Q: How do I check my work when simplifying an algebraic expression?
A: To check your work, you need to plug in a value for the variable and evaluate the expression. If the result is correct, then your simplification is correct.
Examples and Practice
Here are some examples and practice problems to help you practice simplifying algebraic expressions:
Example 1
Simplify the expression (2x² + 3x - 4) - (x² - 2x + 1)
Solution
(2x² + 3x - 4) - (x² - 2x + 1) = 2x² - x² + 3x + 2x - 4 - 1 = x² + 5x - 5
Example 2
Simplify the expression (3y² + 2y - 1) - (2y² - 3y + 2)
Solution
(3y² + 2y - 1) - (2y² - 3y + 2) = 3y² - 2y² + 2y + 3y - 1 - 2 = y² + 5y - 3
Final Thoughts
Simplifying algebraic expressions is an essential skill for any math enthusiast. By understanding the distributive property, combining like terms, and checking your work, you can simplify complex expressions and make them easier to work with. Remember to practice regularly to become proficient in simplifying algebraic expressions.
Additional Resources
Here are some additional resources to help you learn more about simplifying algebraic expressions:
- Algebra textbooks: There are many algebra textbooks available that provide detailed explanations and examples of simplifying algebraic expressions.
- Online resources: There are many online resources available that provide tutorials, examples, and practice problems for simplifying algebraic expressions.
- Math software: There are many math software programs available that can help you simplify algebraic expressions and provide step-by-step solutions.
Conclusion
Simplifying algebraic expressions is a fundamental concept in mathematics, and it requires practice and patience to become proficient. By understanding the distributive property, combining like terms, and checking your work, you can simplify complex expressions and make them easier to work with. Remember to practice regularly and seek additional resources to help you learn more about simplifying algebraic expressions.