7.2 Multiplying Polynomials
This is a set of guiding questions and materials for creating your own lesson plan on how to
multiply polynomials.
Learning Objectives
 To multiply polynomials by a monomial (including constants).
 To multiply two binomials.
 To multiply any two polynomials.
Guiding Questions
 What is (2x)(3y)? What properties did you use?
 Are constants monomials?
 What is 3(7x + 2)? What happens in this case: 3(2+7)?
 How would you multiply two binomials? What about (2 + 3)(5 + 4)?
 How can we extend that to (2x + 3)(5x + 4)?
 What about (2x + 3)(5x – 4)?
 What about (2x – 3)(5x – 4)?
 What about (2x + 3)2?
 How can we extend this to other polynomials, for instance, (3x + 2)(4x2 + x – 7)?
Notes for Teachers
 It is appropriate to review (or introduce?) associativity and commutativity when
exploring how to multiply two monomials.
 When introducing the basic operations, do them first without variables. For instance,
3(2+7) = 6 + 21 = 3(9) = 27.
Video of the Day
 7.2.1 Multiplying two binomials
o Description: Clear and effective approach to learning how to multiply two
binomials based on decomposing integers.
o Tags: binomials, multiplication of two binomials, integer decomposition, FOIL
method
 7.2.2 Squaring a binomial
o Description: Clear and effective approach to learning and remembering how to
square a binomial.
o Tags: binomials, squaring a binomial, integer decomposition, FOIL method
 7.2.3 Multiplying any two polynomials
o Description: Clear and effective approach to learning and remembering how to
multiply polynomials.
o Tags: binomials, multiplication of polynomials, integer decomposition
Exercises and Problems
 North Carolina Common Core Math 1 Item Bank, Nagy-Lup, pp. 15-17
 The width of a rectangle is (2x + 3) and the length is four times its width? What is the
area of the rectangle in terms of x? What advantage does that offer?
 The width of a rectangle is (5x + 2) and the length is three times its width. What is the
area of the rectangle in terms of x?

The base of a triangle is (2x + 9) and the corresponding height is (2x + 5). What is the
area of the rectangle in terms of x? How do you show that the area of a triangle is what
you say it is?
Online Resources
 Regents Prep: Multiplying binomials