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The Distributive Property quiz

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  • What does the distributive property allow you to do with multiplication and parentheses?
    It allows you to distribute multiplication to each term inside the parentheses.
  • How does the distributive property work with subtraction inside parentheses?
    You distribute the multiplication to both terms, treating subtraction as adding a negative, so a(b - c) = ab - ac.
  • What is the result of applying the distributive property to 2 × (4 + 5)?
    It becomes 2 × 4 + 2 × 5, which simplifies to 8 + 10 = 18.
  • Why is the distributive property useful when variables are involved?
    Because you can't combine variables and numbers directly, so you must distribute multiplication to each term.
  • How do you write 4(x - 8) without parentheses using the distributive property?
    It becomes 4x - 32.
  • If you have a constant on the right side of the parentheses, can you still use the distributive property?
    Yes, because multiplication is commutative, so the order does not matter.
  • What is the simplified form of (4x + 2y - 7z) × 3 using the distributive property?
    It is 12x + 6y - 21z.
  • Does the distributive property work with more than two terms inside the parentheses?
    Yes, you distribute the multiplication to every term inside the parentheses.
  • What is the general form of the distributive property for addition?
    a(b + c) = ab + ac.
  • What is the general form of the distributive property for subtraction?
    a(b - c) = ab - ac.
  • Why can't you simplify 4(x - 8) by combining x and 8?
    Because x is a variable and its value is unknown, so you can't perform the subtraction.
  • What property of multiplication allows you to distribute a constant from either side of the parentheses?
    The commutative property of multiplication.
  • How do you distribute 3 to each term in (4x + 2y - 7z)?
    Multiply 3 by each term: 3 × 4x, 3 × 2y, and 3 × (-7z).
  • What is the result of distributing 3 to -7z?
    It is -21z.
  • What does the distributive property help you do with algebraic expressions?
    It helps you simplify expressions by removing parentheses and combining like terms.