What is Factorisation by Regrouping Terms? | Simple Explanation for Class 6

S3-SA1-0249

What is the Factorisation by Regrouping Terms?

Grade Level:

Class 6

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

Definition

What is it?

Factorisation by Regrouping Terms is a method used to break down an algebraic expression into simpler parts (factors) when there isn't a common factor in all terms. We group terms that share a common factor, factor them separately, and then find a common binomial factor.

Simple Example

Quick Example

Imagine you have a list of ingredients for a special chai: 'sugar + ginger + tea leaves + milk'. If you want to group them to make two separate mixes, you might group (sugar + tea leaves) and (ginger + milk) if that helps simplify things later. Similarly, in maths, we group terms like (ax + ay) and (bx + by) to find common parts.

Worked Example

Step-by-Step

Let's factorise: 2x + 6y + ax + 3ay

1. Look for terms that share a common factor. Here, 2x and 6y share '2', and ax and 3ay share 'a'.
---
2. Group the terms: (2x + 6y) + (ax + 3ay)
---
3. Factor out the common factor from each group:
From (2x + 6y), take out 2: 2(x + 3y)
From (ax + 3ay), take out a: a(x + 3y)
---
4. Now the expression is: 2(x + 3y) + a(x + 3y)
---
5. Notice that (x + 3y) is common to both new terms. Factor out this common binomial:
(x + 3y)(2 + a)
---
6. The factors are (x + 3y) and (2 + a).

Answer: (x + 3y)(2 + a)

Why It Matters

This skill is super important for solving complex problems in many fields! Engineers use it to simplify equations for building bridges or designing apps. Data Scientists use it to make sense of large datasets, like predicting cricket scores. Even computer programmers use it to write efficient code.

Common Mistakes

MISTAKE: Not finding a common binomial after grouping. Students might get 2(x + 3y) + a(x + 2y) and get stuck. | CORRECTION: If the binomials are not identical, check your initial grouping or your factoring from each group. The goal is to get the same bracket twice.

MISTAKE: Incorrectly factoring out negative signs. For example, factorising -3x - 6y as -3(x - 2y). | CORRECTION: When factoring out a negative number, remember to change the sign of each term inside the bracket. So, -3x - 6y becomes -3(x + 2y).

MISTAKE: Not rearranging terms when the initial grouping doesn't work. Students might stick to the original order even if it doesn't lead to a common binomial. | CORRECTION: If your first attempt at grouping doesn't yield a common binomial, try rearranging the terms of the original expression and then regrouping.

Practice Questions

Try It Yourself

QUESTION: Factorise: ab + ac + 3b + 3c | ANSWER: (b + c)(a + 3)

QUESTION: Factorise: 5x - 5y + ax - ay | ANSWER: (x - y)(5 + a)

QUESTION: Factorise: 2p^2 + 3pq - 2pr - 3qr | ANSWER: (2p + 3q)(p - r)

MCQ

Quick Quiz

Which of the following is the correct factorisation of 4x + 8y + ax + 2ay?

(x + 2y)(4 + a)

(x + y)(4 + 2a)

4(x + 2y) + a(x + y)

(4x + a)(y + 2)

The Correct Answer Is:

Group (4x + 8y) and (ax + 2ay). Factor out 4 from the first group to get 4(x + 2y). Factor out 'a' from the second group to get a(x + 2y). Then, factor out the common binomial (x + 2y) to get (x + 2y)(4 + a).

Real World Connection

In the Real World

Imagine a logistics company like Delhivery or Ecom Express sorting packages. They might group packages by destination (e.g., all Mumbai packages together) and then by size (e.g., small Mumbai packages). This grouping and regrouping helps them simplify the complex task of delivery, much like how factorisation by regrouping simplifies algebraic expressions to solve problems faster.

Key Vocabulary

Key Terms

FACTOR: A number or expression that divides another number or expression evenly | TERM: A single number, variable, or product of numbers and variables | EXPRESSION: A combination of numbers, variables, and operation symbols | BINOMIAL: An algebraic expression with two terms

What's Next

What to Learn Next

Great job understanding regrouping! Next, you should learn about 'Factorisation using Identities'. This builds on your current knowledge by showing you special patterns that make factorisation even quicker and easier for certain types of expressions.