Summary: Performing Operations on Polynomials

Key Concepts
  • Given multiple polynomials, how to add or subtract them to simplify the expressions

    1. Combine like terms.
    2. Simplify and write in standard form.
  • Use the FOIL method for multiplying two binomials.
    Step 1. Multiply the First terms.  

    Parentheses a plus b times parentheses c plus d is shown. Above a is first, above b is last, above c is first, above d is last. There is a brace connecting a and d that says outer. There is a brace connecting b and c that says inner.
    Step 2. Multiply the Outer terms.
    Step 3. Multiply the Inner terms.
    Step 4. Multiply the Last terms.
    Step 5. Combine like terms, when possible.
  • Multiplying Two Binomials: To multiply binomials, use the:
    • Distributive Property
    • FOIL Method
    • Vertical Method
  • Multiplying a Trinomial by a Binomial: To multiply a trinomial by a binomial, use the:
    • Distributive Property
    • Vertical Method