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Factoring Special Products quiz

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  • What is the factored form of a difference of squares, a^2 - b^2?
    It factors as (a + b)(a - b).
  • What two criteria must be met to use the difference of squares factoring rule?
    Both terms must be perfect squares and have opposite signs.
  • Can the expression a^2 + b^2 be factored using the difference of squares rule?
    No, because it is a sum of squares, not a difference.
  • How would you factor x^2 - 4 using the difference of squares?
    It factors as (x + 2)(x - 2).
  • What is the general form of a perfect square trinomial?
    It is a^2 ± 2ab + b^2.
  • How do you factor a^2 + 2ab + b^2?
    It factors as (a + b)^2.
  • How do you factor a^2 - 2ab + b^2?
    It factors as (a - b)^2.
  • What must be true about the first and last terms in a perfect square trinomial?
    They must both be perfect squares.
  • What must the middle term of a perfect square trinomial equal?
    It must equal 2ab, where a and b are the square roots of the first and last terms.
  • How would you factor x^2 + 10x + 25?
    It factors as (x + 5)^2.
  • How would you factor 4x^2 - 36x + 81?
    It factors as (2x - 9)^2.
  • What is the factored form of a sum of cubes, a^3 + b^3?
    It factors as (a + b)(a^2 - ab + b^2).
  • What is the factored form of a difference of cubes, a^3 - b^3?
    It factors as (a - b)(a^2 + ab + b^2).
  • What does the SOAP acronym stand for when factoring cubes?
    It stands for Same, Opposite, Always Positive, describing the signs in the factors.
  • How would you factor 27y^3 - 1?
    It factors as (3y - 1)(9y^2 + 3y + 1).