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Factoring Special Products definitions

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  • Difference of Squares
    A binomial with two perfect square terms separated by subtraction, factored as the product of conjugates.
  • Perfect Square Trinomial
    A trinomial where the first and last terms are perfect squares and the middle term equals twice their product.
  • Sum of Cubes
    An expression with two perfect cubes added together, factored using a specific binomial and trinomial pattern.
  • Difference of Cubes
    An expression with two perfect cubes subtracted, factored using a binomial and trinomial with SOAP sign rules.
  • Conjugates
    Two binomials with identical terms but opposite signs, whose product yields a difference of squares.
  • SOAP Rule
    A sign pattern acronym: Same, Opposite, Always Positive, used when factoring sums or differences of cubes.
  • Perfect Square
    A term that results from squaring a single expression, such as x² or 25.
  • Perfect Cube
    A term that results from cubing a single expression, such as x³ or 8.
  • Binomial
    A polynomial with exactly two terms, often used in special product patterns.
  • Trinomial
    A polynomial with exactly three terms, commonly seen in perfect square and cube factoring.
  • Factored Form
    A polynomial written as a product of simpler polynomials, revealing its roots or structure.
  • Sign Value
    The positive or negative nature of a term, crucial for applying correct factoring formulas.
  • Coefficient
    A numerical factor multiplying a variable in a term, important for identifying patterns in factoring.
  • Exponent
    A number indicating how many times a base is used as a factor, key for recognizing squares and cubes.
  • Base
    The expression or number being raised to a power in a term, essential for identifying perfect squares or cubes.