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Algebra I Recipe: Multiplying Polynomials
A. Multiplying a Monomial and a Polynomial
  1. Change subtraction to adding the opposite when necessary.
  2. Distribute the monomial to each term of the polynomial.
  3. Remember to add exponents when multiplying like bases and leave the terms in the order as they come after multiplying.
–4x(-18 – 23y)

–x(2x2 - 3x)

B. Multiplying a Binomial and a Binomial
  1. Use the distributive property – F O I L
    • F – the product of the two first terms.
    • O – the product of the two outside terms
    • I – the product of the two inside terms.
    • L – the product of the two last terms.
  2. Combine like terms.
  3. Arrange terms in alphabetical or descending order.
(x + 2) (x – 5)

(5x - 6) (3x + 9)

(7x – 4) (2x – 3)

C. Multiplying Larger Polynomials
  1. Write the smaller polynomial first.
  2. Distribute each term of the smaller polynomial to each term of the larger polynomial.
  3. Combine like terms.
  4. Arrange terms in proper order.
(x + 3) (6 - 3x + 2x2)

(2x + 7) (5x2 + 11x - 8)

(3x2 + 7x – 2) (5x2 - 4x + 1)

G Redden

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