MathematicsChapter 4: Factorization and Algebraic Manipulation
Common Monomial
Look at every term. If k divides each of them, write ka + kb + kc = k(a + b + c).
Learning objectives
- Define and explain common monomial.
- Apply common monomial to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
Look at every term. If k divides each of them, write ka + kb + kc = k(a + b + c). The common monomial k might be 5, or x, or 3xy. Take the highest power of each letter that truly appears in every term, and the greatest common numerical factor. Do not pull out a letter that is missing from one term.
Formula
kc = k(a + b + c). The common monomial k migh
Where / symbols
- Common Monomial
- Look at every term. If k divides each of them, write ka + kb + kc = k(a + b + c). The common monomial k might be 5, or x, or 3xy. Take the highest power of each letter that truly appears in every term, and the greatest common numerical factor. Do not pull out a letter that is missing from one term.
Relationship
- ka + kb + kc = k(a + b + c)
Overview
Learn the idea, then use it:
Core Understanding
Look at every term. If k divides each of them, write ka + kb + kc = k(a + b + c). The common monomial k might be 5, or x, or 3xy. Take the highest power of each letter that truly appears in every term, and the greatest common numerical factor. Do not pull out a letter that is missing from one term.
Examples ka + kb + kc = k(a + b + c) · common monomial · product of factors · COMMON MONOMIAL: Look at every term. If k divides each of them, write ka + kb + kc = k(a + b + c). The common monomial k might be 5, or x
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 — COMMON MONOMIAL
Look at every term. If k divides each of them, write ka + kb + kc = k(a + b + c). The common monomial k might be 5, or x, or 3xy. Take the highest power of each letter that truly appears in every term, and the greatest common numerical factor. Do not pull out a letter that is missing from one term.
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 common monomial with a neighbouring idea that uses a different definition, rule, or method.
Key points
- ka + kb + kc = k(a + b + c)
- common monomial
- product of factors
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Common Monomial
Sticky Notes · Quick Revision
Core Idea
- Look at every term.
Key Points
- ka + kb + kc = k(a + b + c)
- common monomial
- product of factors
Simple Check
- Explain common monomial 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 common monomial 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
- Look at every term.
- ka + kb + kc = k(a + b + c)
- common monomial
- product of factors
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