The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 5.5: Multiplying Monomials

When students multiply monomials, two errors are common. They may multiply the exponents

rather than add them or they may add the coefficients rather than multiply them.

1. Discuss the meaning of bases, exponents, and coefficients. Explain that 3y^2 means 3×y×y.
   yis the base. The exponent 2 meansyis a factor 2 times. The coefficient 3 means 3 groups of
   y×y.


2. Explain that the product of 3y^2 × 5 y^4 can be written as 3×y×y× 5 ×y×y×y×y,which
   equals 15×y^6 or 15y^6. Note that the property of exponents for multiplication,xm·xn=
   xm+n, is a shortcut for finding this product. Also note the following:
   
   
   • If the bases are the same, students can find the product of the bases by adding the
     exponents.
   
   
   • The property of exponents applies only if the bases are the same.
   
   
   • Unless otherwise noted, the exponent of a variable is understood to be 1.
   
   
   • The coefficients of the monomials are not exponents and should be multiplied.
   
   
   
   


3. Review the information and examples on the worksheet with your students. Demonstrate
   how the property of exponents is applied to the problems.

EXTRA HELP:

Placing monomials in parentheses next to each other is another way to show multiplication.

ANSWER KEY:

(1)y^6 (2) 14 a^11 (3)− 18 a^6 (4) 21 a^3 b^3 (5)− 16 a^8 b^3 (6) 24 x^3 y^5 (7) 126 a^3 b^6

(8)− 120 a^5 b^5

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(Challenge)Margo’s answer is correct but there is a flaw in her reasoning. She should have

------------------------------------------------------------------------------------------multiplied the coefficients instead of adding them.

184 THE ALGEBRA TEACHER’S GUIDE