Algebra 1 Honors Lesson

Multiplying Polynomials: From Monomials to Special Cases

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9-10BTC Style / Thinking Classrooms7-2 and 7-3 A1.PAFR.1.4 Add, subtract, and multiply polynomials with initial terms up to a degree of 2.90 min

Learning Objective

Students will multiply polynomials with initial terms up to degree 2, including monomial × monomial, monomial × polynomial, binomial × binomial, and special product patterns, producing results in standard form.

Lesson Overview

Students progress from multiplying a monomial by a monomial, through distributing a monomial over a binomial/trinomial, to multiplying two binomials using area models and FOIL, culminating in the special cases (perfect square trinomials and difference of squares). Each task changes exactly one variable at a time.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Rulers (for drawing area model grids)
Printed area model templates (optional)
Random grouping cards

Scaffolded Task Progression

1Task 1

Simplify each product. Write your answer as a single term.
a)

x^{2} \cdot x^{3}

3 x \cdot 4 x

- 2 x^{2} \cdot 5 x

What rule are you using each time?

2Task 2

Simplify each product.
a)

3 x^{2} \cdot (- 4 x^{2})

- 5 x \cdot (- 2 x^{3})

6 x^{2} \cdot x^{0}

Remember:

x^{0} = 1

. Does that change your approach?

3Task 3

Distribute the monomial. Write each product in standard form.
a)

3 x (x + 4)

- 2 x (5 x - 3)

4 x^{2} (x - 7)

Use the area model below to check part (a). [ Interactive graph / diagram, available in the full lesson ]

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