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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.
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Difference of Squares
What is it?
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.
In simple words
- a2 - b2 = (a - b)(a + b).
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
Important terms
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.
What you should learn
- 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.
Examples
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
CORE UNDERSTANDING
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.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 9
Full school-level explanation
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.
Learn the idea, then use it:
WHAT — 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.
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.
CORE UNDERSTANDING
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.
Remember
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
Examples
- a2 - b2 = (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.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
- keep the ideas separate
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
- correct term
Deeper understanding
Go beyond memorising Difference of Squares. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
- keep the ideas separate
- 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 s
- WHAT — 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 s
Do not merge difference of squares with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Difference of Squares: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
- keep the ideas separate
Important formulas
- a2 - b2 = (a - b)(a + b)
- (a + b)^2 - c^2
- (a + b)^2
Common exam traps
- Do not merge difference of squares with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge difference of squares with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge difference of squares with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
a2 - b2 = (a - b)(a + b)
(a + b)^2 - c^2
(a + b)^2
keep the ideas separate
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)(
a2 - b2 = (a - b)(a + b)
- Definition
- 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)(
- Formula
- a2 - b2 = (a - b)(a + b)
- Example
- a2 - b2 = (a - b)(a + b)
- Critical warning
- Do not merge difference of squares with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Difference of Squares.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Difference of Squares and say why it fits.
Mistake
Q4. State one common mistake students make about Difference of Squares.
Exam note
Q5. Write a short exam note on Difference of Squares: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.