MathematicsChapter 4: Factorization and Algebraic Manipulation
Difference of Squares
a^2 - b^2 = (a - b)(a + b).
Learning objectives
- Define and explain difference of squares.
- Apply difference of squares to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
a2 - b2 = (a - b)(a + b). There is no middle term. Also treat (a + b)^2 - c^2 as a difference of squares whose first piece is already a binomial: (a + b - c)(a + b + c). Any even power minus an even power may factor this way more than once, such as x^4 - 16.
Where / symbols
- Difference Of Squares
- a^2 - b^2 = (a - b)(a + b). There is no middle term. Also treat (a + b)^2 - c^2 as a difference of squares whose first piece is already a binomial: (a + b - c)(a + b + c). Any even power minus an even power may factor this way more than once, such as x^4 - 16.
Relationship
- a2 - b2 = (a - b)(a + b)
Overview
Learn the idea, then use it:
Core Understanding
a2 - b2 = (a - b)(a + b). There is no middle term. Also treat (a + b)^2 - c^2 as a difference of squares whose first piece is already a binomial: (a + b - c)(a + b + c). Any even power minus an even power may factor this way more than once, such as x^4 - 16.
Examples a^2 - b^2 = (a - b)(a + b) · (a + b)^2 - c^2 · (a + b)^2 · DIFFERENCE OF SQUARES: a^2 - b^2 = (a - b)(a + b). There is no middle term. Also treat (a + b)^2 - c^2 as a difference of squares whose first p
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — DIFFERENCE OF SQUARES
a2 - b2 = (a - b)(a + b). There is no middle term. Also treat (a + b)^2 - c^2 as a difference of squares whose first piece is already a binomial: (a + b - c)(a + b + c). Any even power minus an even power may factor this way more than once, such as x^4 - 16.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge difference of squares with a neighbouring idea that uses a different definition, rule, or method.
Key points
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Difference of Squares
Sticky Notes · Quick Revision
Core Idea
- a2 - b2 = (a - b)(a + b).
Key Points
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
Simple Check
- Explain difference of squares in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge difference of squares with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- a2 - b2 = (a - b)(a + b).
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
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