Difference of Squares
A square minus a square factors into conjugates.
Key idea
A square minus a square factors into conjugates.
In depth
a² − b² = (a + b)(a − b). It comes from expanding the product, where the cross terms cancel. Only works for a difference, not a sum.
Worked example
x² − 49 = (x − 7)(x + 7). And 4x² − 9 = (2x − 3)(2x + 3).
Formula
Real-world uses
- Quick mental maths such as 52 × 48 = 50² − 2²
- Simplifying expressions in algebra and calculus
Common mistake
Trying to factor a² + b² with real numbers. It does not factor.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Difference of Squares?
A square minus a square factors into conjugates. It is a topic at the intermediate level in Algebra.
What is the formula for Difference of Squares?
The key formula is a²−b² = (a−b)(a+b).
Where is Difference of Squares used in real life?
Real-world examples: Quick mental maths such as 52 × 48 = 50² − 2²; Simplifying expressions in algebra and calculus.
What should I learn before Difference of Squares?
Make sure you are comfortable with Factoring by Grouping, the previous topic in Algebra.
What is a common mistake with Difference of Squares?
Trying to factor a² + b² with real numbers. It does not factor.
How can I practise Difference of Squares?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Difference of Squares?
Move on to Sum and Difference of Cubes next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.