Unlocking the Power of Factoring: Using the Distributive Property

Algebra 1 Grades High School 6:13 Video
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Lesson Description

Learn how to factor algebraic expressions by applying the distributive property to extract the greatest common factor. This lesson builds upon your understanding of factors and prime factorization from earlier math courses and extends it to algebraic expressions. Factoring is a key skill in algebra, allowing you to simplify expressions and solve equations more easily.

Video Resource

Factoring algebraic expressions using the distributive property | Algebra I | Khan Academy

Khan Academy

Duration: 6:13
Watch on YouTube

Key Concepts

  • Factors and Factoring
  • Greatest Common Factor (GCF)
  • Distributive Property (Undoing)

Learning Objectives

  • Students will be able to identify factors of numbers and algebraic expressions.
  • Students will be able to factor out the greatest common factor from an algebraic expression using the distributive property.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of factors with numerical examples (e.g., factors of 12). Discuss prime factorization as breaking down a number into its prime factors. Explain that this lesson will extend the idea of factoring to algebraic expressions.
  • Video Viewing (10 mins)
    Play the Khan Academy video: 'Factoring algebraic expressions using the distributive property'. Encourage students to take notes on key vocabulary and examples.
  • Guided Practice (15 mins)
    Work through examples similar to those in the video, demonstrating how to factor out the greatest common factor. Start with simpler expressions (e.g., 2 + 4x) and progress to more complex ones (e.g., 6x + 30, 1/2 - 3/2x, AX + AY). Emphasize the 'undoing' of the distributive property. Show how to verify answer by distributing.
  • Independent Practice (15 mins)
    Provide students with a worksheet or online practice problems to solve individually. Offer assistance as needed and circulate to monitor understanding.
  • Wrap-up and Review (5 mins)
    Summarize the key concepts of the lesson and address any remaining questions. Preview the next lesson on more advanced factoring techniques.

Interactive Exercises

  • Factor Frenzy
    Present students with a series of algebraic expressions on the board. Have them race to factor out the GCF correctly. This can be done individually or in teams.
  • Distributive Property Check
    After factoring an expression, have students use the distributive property to multiply the factored expression and verify that it equals the original expression.

Discussion Questions

  • What is a factor, and how does it relate to multiplication?
  • How can you identify the greatest common factor in an algebraic expression?
  • Why is factoring a useful skill in algebra?
  • How is factoring related to the distributive property?

Skills Developed

  • Factoring Algebraic Expressions
  • Applying the Distributive Property
  • Identifying Greatest Common Factors
  • Simplifying Expressions

Multiple Choice Questions

Question 1:

Which of the following is a factor of 15?

Correct Answer: 5

Question 2:

What is the greatest common factor (GCF) of 6x and 9?

Correct Answer: 3

Question 3:

Which expression is equivalent to 2x + 4 after factoring out the GCF?

Correct Answer: 2(x + 2)

Question 4:

Factoring is essentially the _______ of the distributive property.

Correct Answer: Reverse

Question 5:

What is the factored form of 3a + 3b?

Correct Answer: 3(a + b)

Question 6:

What is the factored form of 12x + 18?

Correct Answer: 6(2x + 3)

Question 7:

What is the first step to factoring any algebraic expression?

Correct Answer: Find the greatest common factor

Question 8:

What is the factored form of x/2 + 3x/2?

Correct Answer: x(1/2 + 3/2)

Question 9:

After you have factored an algebraic expression how can you check to make sure you are correct?

Correct Answer: Use the distributive property

Question 10:

What is the factored form of 5x + 10y?

Correct Answer: 5(x + 2y)

Fill in the Blank Questions

Question 1:

A __________ is a number that divides evenly into another number.

Correct Answer: factor

Question 2:

The greatest common factor is the __________ factor that divides into all terms of an expression.

Correct Answer: largest

Question 3:

Factoring is the opposite of __________.

Correct Answer: distributing

Question 4:

In the expression 4x + 8, the GCF is __________.

Correct Answer: 4

Question 5:

When we factor out the GCF from an expression, we are __________ the distributive property.

Correct Answer: undoing

Question 6:

If you factor 3x + 6 and get 3(x+3), then you have done it __________.

Correct Answer: incorrectly

Question 7:

The factored form of 5x+5y is __________.

Correct Answer: 5(x+y)

Question 8:

When you factor you are breaking an expression into two of its __________.

Correct Answer: factors

Question 9:

The factored form of x/4 + 3x/4 is x/4(__________)

Correct Answer: 1+3

Question 10:

The factored form of 20x+30 is __________

Correct Answer: 10(2x+3)

Educational Standards

A1.A.3.3:Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1. A1.A.3.2:Simplify polynomial expressions by adding, subtracting, or multiplying. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

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