Factorisation — Lesson
1) Hook — The Cricket Team Mystery!
Imagine you are the coach of an under-13 cricket team in Mumbai. You have 24 players, and you want to divide them into equal groups for practice matches. But you want to find all the possible ways to split the team evenly. How do you do it quickly without listing every single combination?
This is where factorisation comes to the rescue! Just like breaking down a cricket team into smaller squads, factorisation breaks down numbers and expressions into their building blocks. Let’s learn how to do it step-by-step!
2) Core Concepts — What is Factorisation?
Factorisation means expressing a number or an algebraic expression as a product of its factors. Factors are numbers or expressions that multiply together to give the original number or expression.
The number 12 can be factorised as:
12 = 3 × 4 = 2 × 6 = 2 × 2 × 3
Here, 2 and 3 are prime factors of 12.
Factorise: 6x + 9
Both terms have a common factor 3:
6x + 9 = 3(2x + 3)
Factorisation helps simplify expressions and solve equations easily.
| Expression | Factorised Form | Explanation |
|---|---|---|
| x² + 5x | x(x + 5) | Common factor x |
| x² - 9 | (x - 3)(x + 3) | Difference of squares |
| x² + 7x + 10 | (x + 5)(x + 2) | Find two numbers that multiply to 10 and add to 7 |
3) Key Formulas/Rules
a × b + a × c = a(b + c)
a² − b² = (a − b)(a + b)
a² + 2ab + b² = (a + b)²
a² − 2ab + b² = (a − b)²
x² + (p + q)x + pq = (x + p)(x + q)
4) Did You Know?
Factorisation is like the “item number” in Bollywood! Just like a hit song can be broken down into beats and rhythms, algebraic expressions can be broken down into factors. Even the famous mathematician Bhāskara II from India (12th century) used factorisation techniques to solve equations — long before calculators existed!
5) Exam Tips
- Always look for the Greatest Common Factor (GCF) first before trying other methods.
- Check for special formulas like difference of squares or perfect square trinomials.
- Practice factorising trinomials by finding two numbers that multiply to the last term and add to the middle term.
- Write your steps clearly — examiners love neat work!
- Common Mistake: Forgetting to factor out a negative sign when the leading coefficient is negative.
- Board Exam Pattern: Factorisation questions usually carry 2-4 marks. They may ask you to factorise expressions or solve quadratic equations by factorisation.
Factorisation — Mcq
Factorisation — Mnemonic
Mnemonic 1: "CF + D = Factor Fun!" ⚽🎬
Remembering the steps of factorisation:
- C - Common Factor निकालो (Find the Common Factor first)
- F - Factorise करो (Factorise the remaining expression)
- D - Difference of squares देखो (Check if it’s a difference of squares)
Think of it like a cricket strategy: First find your best bowler (common factor), then bowl your yorkers (factorise), and finally catch the batsman out with a clever trick (difference of squares)! 🏏
Mnemonic 2: "BFF = Binomial Factor Friends" 🎥🍿
For remembering special factorisation formulas:
- B - Binomial square: (a ± b)² = a² ± 2ab + b²
- F - First and last: a² - b² = (a + b)(a - b)
- F - Factor by grouping: Group terms and factor common parts
Just like Bollywood BFFs, these formulas always stick together to make factorisation easy and fun! 🎬👫
Mnemonic 3: "FACTOR का SECRET 🔍" (Hindi rhyme)
"पहले निकालो Common Factor,
फिर देखो Square का Actor,
Last में करो Grouping का Sector,
Factorisation होगा Perfectector!" 🎉
Translation: First find the common factor, then spot the square’s actor (difference of squares), lastly do grouping’s sector — and your factorisation will be perfect!
Mission: Master This Topic!
Reinforce what you learned with fun activities
Ready to Battle? Test Your Knowledge!
Practice MCQs, build combos, climb the leaderboard!
Start Practice