Simplifying Variable Expressions
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Questions and Answers

What is the simplified form of the expression $4x + 3$?

  • $4x + 3$ (correct)
  • $4x + 6$
  • $7x$
  • $4x$

    • Which expression simplifies to $2x^2 + 40x + 12$?

  • $2x(x + 20) + 12$
  • $4x^2 + 20x + 6$
  • $2(x^2 + 20x + 6)$ (correct)
  • $x(2x + 40) + 12$

    • What is the result of simplifying $-5x^2 - 12x + 4$?

  • $-5x^2 - 12x + 4$ (correct)
  • $-5x^2 + 12x + 4$
  • $-12x^2 + 4x$
  • $-x^2 - 4x + 4$

    • What is the simplified form of $90x - 48$?

    <p>$6(15x - 8)$ (D)</p> Signup and view all the answers

    Which expression represents $2x^2 - 12x$ simplified?

    <p>$2x(x - 6)$ (D)</p> Signup and view all the answers

    What is the simplified result of the expression $3(𝑥 + 9)$?

    <p>$3x + 27$ (C)</p> Signup and view all the answers

    What is the result of simplifying $7𝑥 + 3 - 3𝑥$?

    <p>$4x + 3$ (D)</p> Signup and view all the answers

    What is the simplified form of the expression $12𝑥 - 3𝑥(𝑥 + 9)$?

    <p>$12x - 3x^2 - 27$ (A)</p> Signup and view all the answers

    When simplifying the expression $8𝑥 - 12𝑥 - 𝑥^2 + 13$, what is the resulting expression?

    <p>$-5x - x^2 + 13$ (B)</p> Signup and view all the answers

    What is the result of the simplification $5𝑥(−8𝑥 + 12) + 14𝑥$?

    <p>$-40𝑥^2 + 60𝑥$ (C)</p> Signup and view all the answers

    Flashcards

    Simplifying expressions

    The process of combining like terms and reducing expressions to their simplest form.

    Distributive property

    Multiplying a single term by each term inside parentheses, e.g., a(b + c) = ab + ac.

    Like terms

    Terms that have the same variable raised to the same power, e.g., 3x and 5x.

    Combining like terms

    The method of adding or subtracting coefficients of like terms to simplify expressions.

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    Variables in expressions

    Symbols like x or y, used to represent unknown values in mathematical expressions.

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    Variable Expression

    An expression that contains variables, coefficients, and constants (e.g., 3x + 4).

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    Coefficient

    A numerical factor that multiplies a variable (e.g., in 4x, 4 is the coefficient).

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    Combine Like Terms

    The method of adding or subtracting coefficients of like terms in an expression.

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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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    Description

    This quiz focuses on simplifying variable expressions using various mathematical techniques. Participants will learn to combine like terms, use the distributive property, and apply exponent rules effectively. Additionally, the quiz covers essential operations in evaluating expressions.

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