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9.2: Multiplication of Polynomials

Difficulty Level: At Grade Created by: CK-12
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Learning Objectives

At the end of this lesson, students will be able to:

  • Multiply a polynomial by a monomial.
  • Multiply a polynomial by a binomial.
  • Solve problems using multiplication of polynomials.



Teaching Strategies and Tips

Use Example 1 to introduce polynomial multiplication beginning with monomials.

  • Have students apply the product rule for exponents to each variable separately.
  • Multiply the coefficients separately.

Use Examples 2 and 3 to show that the product of a monomial and any polynomial uses the distributive property.

  • Show why the distributive property works by finding the area of a rectangle in two ways. See illustration preceding Example 2.
  • After distributing, students use the method to multiply two monomials.

Use Examples 4 and 5 to demonstrate the product of two binomials. There are two approaches:

  • In-line or horizontal multiplication. Use the distributive property as before.
  • Vertical multiplication. Arrange like terms in columns. Draw the analogy to the method of multiplying two integers that students learned in grade school.

Error Troubleshooting

General Tip: Remind students to combine like terms after multiplying. Have them check their answer and make sure all like terms have been combined.

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