Operations on Polynomials

  1. Addition and Subtraction of Polynomials
    1. Methods of Organizing Polynomials
      1. Descending Order : Arranging a polynomial by the powers of one variable from highest to lowest degree.
      2. Ascending Order : Arranging a polynomial by the powers of one variable from lowest to highest degree.
    2. Addition and Subtraction of Polynomials
      1. Addition : Combine like terms.
      2. Subtraction : Change the sign of each term in the polynomial being subtracted, then add.
    3. Properties of Polynomial Addition
      For three polynomials , , and :
      1. Commutative Property:
      2. Associative Property:

  2. Multiplication of Polynomials
    1. Multiplication of Polynomials:
      Use the distributive property and the laws of exponents to expand the expression, then combine like terms.
    2. Properties of Polynomial Multiplication
      For three polynomials , , and
      1. Commutative Property:
      2. Associative Property:
      3. Distributive Property:
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  3. Multiplication Formulas







  4. Modified Multiplication Formulas









  • Multiplication Formulas