What is Factorisation? | Simple Explanation for Class 6

S3-SA1-0247

What is the Factorisation of Algebraic Expressions?

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Factorisation of algebraic expressions is like breaking down a number into its prime factors, but for expressions with variables. It means writing an algebraic expression as a product of two or more simpler expressions (called factors). Think of it as finding the building blocks of an expression.

Simple Example

Quick Example

Imagine you have 6 mangoes and your friend has 9 mangoes. The total mangoes are 6 + 9 = 15. But what if we want to share them equally among some friends? We can say 6 mangoes is 2 x 3, and 9 mangoes is 3 x 3. Both have '3' as a common factor. So, (6 + 9) can be written as 3 x (2 + 3), which is 3 x 5 = 15. Here, '3' and '(2 + 3)' are the factors of 15. Similarly, for algebraic expressions, we find common factors.

Worked Example

Step-by-Step

Let's factorise the expression: 4x + 8y

1. Look for common factors in the numbers (coefficients) and variables in each term. Here, the terms are 4x and 8y.
---2. For the numbers, 4 and 8, the greatest common factor (GCF) is 4. (Because 4 = 4 x 1 and 8 = 4 x 2).
---3. For the variables, 'x' and 'y' are different, so there are no common variables.
---4. The common factor for the entire expression is 4.
---5. Now, write the common factor outside a bracket: 4( ).
---6. Divide each original term by the common factor: (4x / 4) = x and (8y / 4) = 2y.
---7. Put these results inside the bracket: 4(x + 2y).
---8. So, the factorised form of 4x + 8y is 4(x + 2y).

Why It Matters

Factorisation helps simplify complex problems, making them easier to solve in various fields. Engineers use it to design structures efficiently, while computer scientists use it in algorithms for faster calculations. It's a fundamental skill for careers in AI/ML, data science, and even cryptography!

Common Mistakes

MISTAKE: Not finding the GREATEST common factor (GCF). For example, factorising 6x + 12 as 2(3x + 6y). | CORRECTION: Always find the largest possible common factor. The GCF of 6 and 12 is 6, so the correct factorisation is 6(x + 2y).

MISTAKE: Forgetting to include all terms inside the bracket after taking out the common factor. For example, factorising 3x + 9 as 3x. | CORRECTION: Remember to divide EACH term by the common factor and place the results inside the bracket. The correct factorisation of 3x + 9 is 3(x + 3).

MISTAKE: Confusing factorisation with expanding an expression. Students sometimes multiply factors instead of finding them. | CORRECTION: Factorisation is the reverse of multiplication. You start with a sum/difference and end with a product of factors.

Practice Questions

Try It Yourself

QUESTION: Factorise the expression: 5a + 10b | ANSWER: 5(a + 2b)

QUESTION: Factorise the expression: 7pq - 14pr | ANSWER: 7p(q - 2r)

QUESTION: Factorise the expression: 12x^2 + 18x | ANSWER: 6x(2x + 3)

MCQ

Quick Quiz

Which of the following is the correct factorisation of 9m + 15n?

3(3m + 5n)

3(9m + 15n)

9(m + 15n)

5(9m + 3n)

The Correct Answer Is:

The greatest common factor of 9 and 15 is 3. When 3 is taken out, 9m becomes 3m (9m / 3) and 15n becomes 5n (15n / 3), so the expression becomes 3(3m + 5n).

Real World Connection

In the Real World

Imagine you're a data analyst for an Indian e-commerce company like Flipkart or Amazon. You might have an expression representing the total cost of items with discounts. Factorisation helps you simplify this expression to quickly calculate costs for different customers or even to find the best discount strategy. For example, if '100x + 150y' is the cost, factorising it to '50(2x + 3y)' makes calculations faster.

Key Vocabulary

Key Terms

FACTOR: A number or expression that divides another number or expression exactly | ALGEBRAIC EXPRESSION: A mathematical phrase that can contain numbers, variables (like x, y), and operators (like +, -, x, /) | TERM: Parts of an algebraic expression separated by + or - signs | COMMON FACTOR: A factor that two or more numbers or expressions share | GREATEST COMMON FACTOR (GCF): The largest common factor of two or more numbers or expressions

What's Next

What to Learn Next

Great job understanding factorisation! Next, you can learn about 'Factorisation by Grouping' and 'Factorisation using Identities'. These build on what you've learned here and will help you factorise even more complex expressions, which is super useful in higher grades!