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Factoring Special Products definitions

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  • Difference of Squares
    A polynomial with two perfect square terms separated by subtraction, factored into the sum and difference of their square roots.
  • Perfect Square Trinomial
    A three-term polynomial where the first and last terms are perfect squares and the middle term equals twice their product.
  • Sum of Cubes
    A polynomial with two perfect cube terms added together, factored into a binomial and a trinomial using the SOAP rule.
  • Difference of Cubes
    A polynomial with two perfect cube terms separated by subtraction, factored into a binomial and a trinomial using the SOAP rule.
  • Conjugates
    Two binomials with identical terms but opposite signs, whose product results in a difference of squares.
  • SOAP Rule
    A sign pattern acronym for factoring cubes: Same, Opposite, Always Positive, guiding sign placement in the trinomial.
  • Binomial
    An algebraic expression consisting of two terms, often used as a factor in special product factorizations.
  • Trinomial
    An algebraic expression with three terms, commonly appearing in perfect square and cube factorizations.
  • Perfect Square
    A term that can be written as the square of another term, crucial for identifying special factoring patterns.
  • Perfect Cube
    A term that can be written as the cube of another term, essential for recognizing sum or difference of cubes.
  • Coefficient
    A numerical factor multiplying a variable, important for checking if terms are perfect squares or cubes.
  • Exponent
    A number indicating how many times a base is used as a factor, key for identifying squares and cubes.
  • Factored Form
    An expression rewritten as a product of simpler polynomials, revealing underlying patterns and structure.
  • Sum of Squares
    A polynomial with two perfect square terms added together, which cannot be factored using special product rules.