Math is Fun: Factoring Algebraic Expressions

Factor Hunt

Display:

12 = 2 × 6

12 = 3 × 4

Ask students:

• What are the factors of 12?
• What are the factors of 18?
• What factors do 12 and 18 have in common?

Next, display:

6x + 12

Ask:

• What number appears in both terms?
• How might we "pull out" that common factor?

What Is Factoring?

Explain:

Factoring is finding what expressions were multiplied together to create a larger expression.

Use the example:

2y + 6

Both terms share a factor of 2.

Therefore:

2y + 6 = 2(y + 3)

Discuss how factoring is the opposite of expanding.

Show:

2(y + 3) = 2y + 6

Introduce vocabulary:

• Factor
• Greatest Common Factor (GCF)
• Expression
• Expand

• Exploring Factoring with Math Is Fun
  Direct students to:

  https://www.mathsisfun.com/algebra/factoring.html

  Students read the sections:

  Factors
  Factoring
  Common Factor
  Difference of Squares
  As a class, review the examples:

  2y+6=2(y+3)2y+6=2(y+3)2y+6=2(y+3)

  and

  4x2−9=(2x+3)(2x−3)4x^2-9=(2x+3)(2x-3)4x2−9=(2x+3)(2x−3)

  Discuss:

  What common factor was removed?
  How do we know the answer is correct?
  Why is factoring the opposite of expanding?

  Factor

Exploring Factoring with Math Is Fun

Direct students to:

https://www.mathsisfun.com/algebra/factoring.html

Students read the sections:

• Factors
• Factoring
• Common Factor
• Difference of Squares

As a class, review the examples:

2y + 6 = 2(y + 3) 2y + 6 = 2(y + 3) 2y + 6 = 2 (y + 3)

and

4 x ² − 9 = (2x + 3)(2x − 3)

Discuss:

• What common factor was removed?
• How do we know the answer is correct?
• Why is factoring the opposite of expanding?

Part A: Common Factors
Factor:

8x + 24
15y + 45
12m² + 24m
18a² + 6a

Students use the webpage examples to guide their work.

Part B: Difference of Squares

After reading the "Difference of Squares" section, factor:

1. x² − 16
2. x² − 49
3. 4x² − 25
4. 9y² − 64

Students refer back to the webpage when needed.

Part C: Website Analysis

Students answer:

1. What is the first step when factoring?
2. Why is the greatest common factor important?
3. What pattern helps identify a difference of squares?
4. How can expanding be used to check factoring?
    

Exit Ticket

Factor the following:

1. 6x + 18
2. 12y² + 24y
3. x² − 36

Short Response:

• What is factoring?
• Why is factoring considered the opposite of expanding?

Success Criteria

Students can:

✓ Identify common factors.

✓ Factor expressions correctly.

✓ Recognize difference of squares.

✓ Verify answers through expansion.

Real-World Algebra

A school fundraiser earns:

12n + 24

where n represents the number of student groups participating.

Factor the expression:

12(n + 2)

Discuss:

• What does the 12 represent?
• Why might factoring make calculations easier?

Reflection
Where might businesses, engineers, or scientists use algebraic expressions and factoring?