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