Mathematical

# What does Factorising Mean in Maths – Example of Factorising Mean

The process of factorising is often used to simplify equations or to find out the greatest common factor. But if your question is, what does factorising mean in maths? And if you want to truly understand factorisation in maths, this blog is just what you were looking for.

We will help you learn about what does factorise mean, examples of factorising, factorise algebraic expressions and many more.

Table of Content

## What is Factorising Mean?

When it comes to maths, we often become confused as to what does factorising means in maths?

In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number.

It is the process of using brackets to represent an expression as the product of its factors. We do this by removing any elements that are shared by all of the expression’s terms.

Expanding brackets is the opposite of factorising. An expression is said to be fully factored in by removing the most common factors when included in brackets.

The easiest method of factoring is:

1. Determine the expression’s terms’ highest common factor.

2. Before any brackets, type the highest common factor (HCF).

3. Multiply out each term to complete each bracket.

For example, the x2 – 4 and the integer 15 can both be factored by the number 3 x 5.

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## Rules of Factorisation Mean

The rules of factorisation involves the following methods:

**Factoring Algebra**

The act of factoring algebraic terms is known as factoring algebra.

To put it simply, it is like dividing an expression into a simpler expressions known as “factoring algebra expressions. For example, 2y + 6 = 2(y + 3).

The following information contains different types of factoring algebra:

**Common Factors Method**

With this technique, we only remove the elements that each expression in the given statement has in common.

For example, factorise 3x + 9.

Due to the fact that 3 is a common factor for both 3x and 9, when we use 3 as a common factor, we get:

3x + 9 = 3(x+3).

**Regrouping of Terms Technique**

Regrouping involves rearranging the given expression using terms that are related or identical to one another.

2xy + 3x + 2y + 3 can be rearranged to become, for example:

2xy + 3x + 2y + 3

Factorising the terms by expanding them.

= 2 × x × y + 3 × x + 2 × y + 3

Adjust to get the common factor

= x × (2y + 3) + 1 × (2y + 3)

We can now remove the common factor (2y + 3).

= (2y + 3) (x + 1)

These are the necessary factors as a result.

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**Using Identities for Factorisation**

we can factorise the given expression, by using the common identities.

For example, factorise 4x^{2} – 9.

Solution:

We know using the algebraic identities;

A^{2} – B^{2} equals (A – B) (A + B)

As a result, we can say,

4x^{2} -9

= (2x)^{2} – 3^{2}

= (2x + 3) (2x -3)

## What Does Factorise Mean in Algebra?

According to CUEMATH the factorisation of algebraic expressions is the process of identifying two or more expressions whose product is the given expression.

### How to Factorise Letters?

Three important techniques used to factorise letters are discussed below:

#### 1. Factoring in just one set of brackets

The algebraic expression can be factored into a single bracket by finding the most common factor between all the terms.

Place one bracket in front of the highest common factor (HCF). By multiplying out, fill in each term in the bracket.

#### 2. Adding double brackets as factors

When two brackets are written next to one another, the brackets must be multiplied together. For example , (y + 2) (y + 3) means (y + 2) (y + 3).

Double bracket expansion requires multiplying each term in the first bracket by each term in the second bracket.

#### 3. Two squares’ differences

When an equation can be factored as (a+b) when considered as the difference of two perfect squares, for example, a^{2}-b^{2} = (a+b) (a-b). For example, factoring x2-25 results in (x+5) (x-5).

## Example of Factorising Mean

Factoring is the opposite of expanding brackets. Therefore, an example would be to change 2x² + x – 3 to (2x + 3) (x – 1).

This method of resolving quadratic equations is crucial. When factorising an expression, the first step is to “take out” any shared factors that the terms share.

Another example of factorising is x^{2} – 4 and the integer 15 can both be factored by the number 3 x 5.

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## GCSE and Functional Skills Factorising Mean

Functional skills are transferable qualities that can be used in a variety of industries and professions. They are requirements for apprenticeships and are on a level with the GCSE.

The GCSE questions and answers below can help you to improve your GCSE exam preparation:

1. Factorise: 9x − 18

Ans: 9(x − 2)

2. Factorise fully: 16x^{2} + 20xy

Ans: 4x(4x + 5y)

3. Factorise fully: 3y^{2} − 4y − 4

Ans: (3y + 2)(y − 2)

### FAQ

#### How do I factories numbers?

You can easily find out the factors of a given number by multiplying it by the lowest prime number (greater than 1) that divides it evenly and leaves no remainder.

#### How do you factor into three brackets?

Just break things down when it comes to triple brackets. Expand the second bracket before multiplying your answer by the third bracket.

#### Why do we factorise?

We factorise because of its usefulness.

For example, if you want to divide an eight-piece pie among four individuals, factoring allows you to calculate that each person should get two pieces of the pie.

#### How do you factorise in the 9th grade?

We do this by removing any elements that are common to all of the expression’s elements.

#### How do you solve factorise questions?

We can use the general factorization formula N = Xa × Yb × Zc to answer a number of questions.

Here, the factors of a factorised number are represented as X, Y, and Z.

#### What is meant by factorization?

It is defined as the process of breaking a quantity down into factors.

#### What are factorising expressions?

Factorising an expression refers to putting it in brackets by removing the most common factors.

#### What are factor pairs?

In order to calculate the original number, factors are frequently presented as pairs of numbers. They are referred to as factor pairs.

#### What are the factors of 100?

Generally, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, and 100.

#### Give an example of factorisation and explain it.

The highest common factor (HCF) among all the terms must be removed in order to fully factorise an expression.

For example, 3 × 5 is a factorization of the integer 15 and is a factorization of the x² – 4.

## Conclusions

In the actual world, factoring is a useful skill. Calculating while travelling, splitting something into equal pieces, exchanging money, comparing costs, and understanding time are some examples of common uses.

The concept of factoring is essential for improving our understanding of different types of equations.

In maths, we want to make things as simple as possible. This is why factorizing is useful. It allows us to make our problems and their answers simpler

I hope this article helped you understand what does factorising mean in maths? better.

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