MathematicsChapter 4: Factorization and Algebraic Manipulation
Substitution
If a polynomial is quadratic in a block, set y equal to that block.
Learning objectives
- Define and explain substitution.
- Apply substitution to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
If a polynomial is quadratic in a block, set y equal to that block. A common Class 9 choice is y = ax2 + bx (sometimes plus a constant). Then an expression in y factors by splitting. After you have (y + m)(y + n), replace y. Substitution does not change the value; it only shortens the writing.
Formula
y = ax2 + bx (sometimes plus a constant). T
Where / symbols
- Substitution
- If a polynomial is quadratic in a block, set y equal to that block. A common Class 9 choice is y = ax^2 + bx (sometimes plus a constant). Then an expression in y factors by splitting. After you have (y + m)(y + n), replace y. Substitution does not change the value; it only shortens the writing.
Relationship
- y = ax2 + bx
Overview
Learn the idea, then use it:
Core Understanding
If a polynomial is quadratic in a block, set y equal to that block. A common Class 9 choice is y = ax2 + bx (sometimes plus a constant). Then an expression in y factors by splitting. After you have (y + m)(y + n), replace y. Substitution does not change the value; it only shortens the writing.
Examples y = ax^2 + bx · Substitution · Substitution · SUBSTITUTION: If a polynomial is quadratic in a block, set y equal to that block. A common Class 9 choice is y = ax^2 + bx (sometimes
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 — SUBSTITUTION
If a polynomial is quadratic in a block, set y equal to that block. A common Class 9 choice is y = ax2 + bx (sometimes plus a constant). Then an expression in y factors by splitting. After you have (y + m)(y + n), replace y. Substitution does not change the value; it only shortens the writing.
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 substitution with a neighbouring idea that uses a different definition, rule, or method.
Key points
- y = ax2 + bx
- Substitution
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Substitution
Sticky Notes · Quick Revision
Core Idea
- If a polynomial is quadratic in a block, set y equal to that block.
Key Points
- y = ax2 + bx
- Substitution
- Substitution
Simple Check
- Explain substitution 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 substitution 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
- If a polynomial is quadratic in a block, set y equal to that block.
- y = ax2 + bx
- Substitution
- Substitution
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