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Multiplying and Factoring Polynomial Expressions




 


Videos to help Algebra I students learn how to use the distributive property to multiply a monomial by a polynomial and understand that factoring reverses the multiplication process. Students use polynomial expressions as side lengths of polygons and find area by multiplying. Students recognize patterns and formulate shortcuts for writing the expanded form of binomials whose expanded form is a perfect square or the difference of perfect squares.

New York State Common Core Math Module 4, Algebra I, Lesson 1, Lesson 2

Related Topics:
Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

Lesson 1 Summary

Factoring is the reverse process of multiplication. When factoring, it is always helpful to look for a GCF that can be pulled out of the polynomial expression. For example, 3ab - 6a can be factored as 3a(b - 2).

Factor the difference of perfect squares a2 - b2 as (a - b)(a + b)
When squaring a binomial (a + b)2 = a2 + 2ab + b2

Lesson 1 Problem Set Sample Solutions

1. For each of the following factor out the greatest common factor:

2. Multiply:

3. The measure of a side of a square is x units. A new square is formed with each side 6 units longer than the original square’s side. Write an expression to represent the area of the new square. (Hint: Draw the new square and count the squares and rectangles.)




Lesson 2 Summary

Multiplying binomials is an application of the distributive property; each term in the first binomial is distributed over the terms of the second binomial.

The area model can be modified into a tabular form to model the multiplication of binomials (or other polynomials) that may involve negative terms.

When factoring trinomial expressions (or other polynomial expressions), it is useful to look for a GCF as your first step.

Do not forget to look for these special cases:

  • The square of a binomial
  • The product of the sum and difference of two expressions.


Lesson 2 Problem Set Sample Solutions

1. Factor these trinomials as the product of two binomials and check your answer by multiplying:

2. The parking lot at Gene Simon’s Donut Palace is going to be enlarged, so that there will be an additional 30 ft. of parking space in the front and 30 ft. on the side of the lot. Write an expression in terms x of that can be used to represent the area of the new parking lot.


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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