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Questions and Answers
What is the simplified form of the expression $4x + 3$?
What is the simplified form of the expression $4x + 3$?
- $4x + 3$ (correct)
- $4x + 6$
- $7x$
- $4x$
Which expression simplifies to $2x^2 + 40x + 12$?
Which expression simplifies to $2x^2 + 40x + 12$?
- $2x(x + 20) + 12$
- $4x^2 + 20x + 6$
- $2(x^2 + 20x + 6)$ (correct)
- $x(2x + 40) + 12$
What is the result of simplifying $-5x^2 - 12x + 4$?
What is the result of simplifying $-5x^2 - 12x + 4$?
- $-5x^2 - 12x + 4$ (correct)
- $-5x^2 + 12x + 4$
- $-12x^2 + 4x$
- $-x^2 - 4x + 4$
What is the simplified form of $90x - 48$?
What is the simplified form of $90x - 48$?
Which expression represents $2x^2 - 12x$ simplified?
Which expression represents $2x^2 - 12x$ simplified?
What is the simplified result of the expression $3(𝑥 + 9)$?
What is the simplified result of the expression $3(𝑥 + 9)$?
What is the result of simplifying $7𝑥 + 3 - 3𝑥$?
What is the result of simplifying $7𝑥 + 3 - 3𝑥$?
What is the simplified form of the expression $12𝑥 - 3𝑥(𝑥 + 9)$?
What is the simplified form of the expression $12𝑥 - 3𝑥(𝑥 + 9)$?
When simplifying the expression $8𝑥 - 12𝑥 - 𝑥^2 + 13$, what is the resulting expression?
When simplifying the expression $8𝑥 - 12𝑥 - 𝑥^2 + 13$, what is the resulting expression?
What is the result of the simplification $5𝑥(−8𝑥 + 12) + 14𝑥$?
What is the result of the simplification $5𝑥(−8𝑥 + 12) + 14𝑥$?
Flashcards
Simplifying expressions
Simplifying expressions
The process of combining like terms and reducing expressions to their simplest form.
Distributive property
Distributive property
Multiplying a single term by each term inside parentheses, e.g., a(b + c) = ab + ac.
Like terms
Like terms
Terms that have the same variable raised to the same power, e.g., 3x and 5x.
Combining like terms
Combining like terms
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Variables in expressions
Variables in expressions
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Variable Expression
Variable Expression
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Coefficient
Coefficient
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Combine Like Terms
Combine Like Terms
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Study Notes
Simplifying Variable Expressions
- Combining Like Terms: Simplify expressions by adding or subtracting terms with the same variables and exponents.
- Distributive Property: Use the distributive property to multiply a coefficient by terms inside parentheses. Example: 3(x + 9) = 3x + 27
- Adding/Subtracting Variable Expressions: Combine like terms to simplify expressions with variables. Example: 7x + 3 - 3x = 4x + 3
- Exponent Rules: When multiplying variables with exponents, add the exponents. When dividing, subtract the exponents.
- Order of Operations (PEMDAS/BODMAS) is essential when evaluating or simplifying complex expressions.
- Combine constants: Add or subtract any constants (numbers without variables)
- Multiple Applications: Simplify expressions containing multiple terms with variables and constants. Example: 12x – 3x(x + 9) = −3x² + 12x - 27
List of Solved Examples (Problems 1-32)
- Problem 1: 3(x + 9) = 3x + 27
- Problem 2: (-6)(8x - 4) = -48x + 24
- Problem 3: 7x + 3 - 3x = 4x + 3
- Problem 4: −2 − x² - 6x2 = −7x² - 2
- Problem 5: 3 + 10x² + 2 = 10x² + 5
- Problem 6: 8x² + 6x + 7x² = 15x² + 6x
- Problem 7: 5x² - 12x² + 8x = -7x² + 8x
- Problem 8: 2x² - 2x – x = 2x² - 3x
- Problem 9: 4x + 6(2 - 5x) = -24x + 12
- Problem 10: 10x + 8(10x – 6) = 90x - 48 and so on for the full list.
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