TOPIC
MY PROGRESS
Pug Score
0%
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Next Steps
Get Started
Get unlimited access to all videos, practice problems, and study tools.
Unlimited practice
Full videos
Back to Menu
Topic Progress
Pug Score
0%
Videos Watched
0/0
Best Practice
No score
Read
Not viewed
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Next Steps
Overview
Grade 10
Develop algebraic reasoning and number sense
8. Demonstrate understanding of common factors and trinomial factoring concretely, pictorially, and symbolically
8.10 Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Difference of Squares
a squared minus b squared always factors as (a minus b) times (a plus b).
What You'll Learn
a squared minus b squared always factors as (a minus b)(a plus b).
The pattern works because the middle terms cancel when you multiply it back out.
Both terms must be perfect squares, separated by subtraction, not addition.
a squared plus b squared does not factor this way.
Example: x squared minus 25 factors as (x minus 5)(x plus 5).
What You'll Practice
1
Factoring binomials with squared variables and constants
2
Multiplying conjugate pairs to produce difference of squares
3
Factoring expressions with higher exponents like x - 16
4
Factoring multi-step problems requiring repeated difference of squares
5
Factoring expressions involving perfect square trinomials and difference of squares
Why This Matters
Mastering difference of squares is essential for simplifying complex algebraic expressions and solving quadratic equations efficiently. This pattern appears throughout algebra, precalculus, and calculus, making it a crucial shortcut that saves time and reduces errors in advanced math.
Before You Start — Make Sure You Can:
This Unit Includes
8 Video lessons
Practice exercises
Learning resources
Skills
Difference of Squares
Factoring
Conjugates
Polynomials
Special Products
Perfect Squares
Algebraic Patterns
MB Curriculum Aligned