Factoring by Grouping
A powerful method to factor polynomials with 4 or more terms
Grade 7 Algebra🤔 When Do We Use Factoring by Grouping?
You've already learned how to factor out a Greatest Common Factor (GCF) from all terms. But what happens when there is no single common factor for all terms?
Use Factoring by Grouping when:
- The polynomial has 4 or more terms
- There is no single common factor shared by ALL terms
- But terms can be grouped into pairs, and each pair has its own common factor
- The groups produce the same binomial factor
📌 Remember: Factoring by grouping is the second method of factoring you learn — right after factoring out a common factor. It's a key tool in your algebra toolbox!
💡 The Key Idea
The Strategy:
- Group terms into pairs
- Factor out the common factor from each pair
- Both pairs should produce the same binomial factor
- Factor out that common binomial
Visual Summary
\( ax + ay + bx + by \)
Group into pairs
\( (\underbrace{ax + ay}_{\text{Group 1}}) + (\underbrace{bx + by}_{\text{Group 2}}) \)
Factor each group
\( a(x + y) \) + \( b(x + y) \)
Factor out the common binomial
\( (x + y)(a + b) \)