Questions and Answers
What is an algebraic expression?
A mathematical statement with at least one operation and a variable
What does it mean to simplify an expression?
To make an expression easier; to combine like terms
What are like terms?
Parts of an algebraic expression that have the same variable raised to the same power
What is the distributive property?
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What is the simplified form of 3x + 4y + 9x + 2y?
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What is the simplified form of 8(2x + 4)?
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What is the simplified form of 2(x + 4) + 4x?
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What is the simplified form of 3x + 5y + 4z^2 + 2x + 3z^2?
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What is the simplified form of 8x^2 + 6x + 9x^3 + 4x + 3x^2 + 2x^3?
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Study Notes
Algebraic Expressions
- An algebraic expression includes at least one operation (addition, subtraction, multiplication, division) and a variable.
Simplification
- Simplifying an expression involves making it easier to understand by combining like terms and removing unnecessary components.
Like Terms
- Like terms share the same variable raised to the same power, enabling them to be combined. Examples include 2x with 3x and 4x² with 6x².
Distributive Property
- This property is utilized to multiply a sum by a number by distributing the multiplier across each term within parentheses. For example, 3(x + 5) becomes 3x + 15.
Examples of Simplifying Expressions
- Simplifying 3x + 4y + 9x + 2y yields 12x + 6y by combining like terms.
- The expression 8(2x + 4) simplifies to 16x + 32 using the distributive property.
- For 2(x + 4) + 4x, simplifying results in 6x + 8.
- The expression 3x + 5y + 4z² + 2x + 3z² simplifies to 5x + 5y + 7z² by combining like terms.
- The simplification of 8x² + 6x + 9x³ + 4x + 3x² + 2x³ results in 11x² + 10x + 11x³.
Key Takeaways
- Understanding how to identify and combine like terms is crucial for simplifying algebraic expressions effectively.
- Mastery of the distributive property is essential for breaking down complex expressions.
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Description
This set of flashcards focuses on key concepts related to simplifying algebraic expressions, including definitions and examples. Understand essential terms like algebraic expression and like terms, and learn the distributive property to enhance your algebra skills.
