## Understanding Factoring an Expression

Factoring allows us to change an expression where terms are added together (or subtracted from each other) to one where they are multiplied together.- On the left-hand side of the equation,
**ab**and**ac**are added together. - On the right-hand side of the equation,
**a**is multiplying**(b + c)**.

**a**, which is common to

**ab**and

**ac**, outside of the bracket. This leaves

**b + c**inside the bracket.

**a**is the Greatest Common Factor of

**ab**and

**ac**. It is the largest factor that is common to the two terms.

## How to Factor an Expression

Factoring an expression is easy.## Question

Factor the expression below.## Step-by-Step:

## 1

Find the Greatest Common Factor of the terms in the expression.
The terms in the expression are

**2x**and^{2}**2xy**.- Look at the number that appears in both terms.
**2**x^{2},**2**xy

- Look at the letters that appear in both terms. In our example, only
**x**appears in both terms. For each letter that appears in both terms, find the letter with the smallest exponent.2**x**, 2^{2}**x**y**x**has the smallest exponent. (**x**has an*implicit*exponent of 1 (**x**=**x**), whereas^{1}**x**has an exponent of 2).^{2}

- Write these terms next to each other.
**2x**is the Greatest Common Factor of**2x**and^{2}**2xy**. Learn more about finding the greatest common factor in algebra

## 2

Write the Greatest Common Factor outside of the brackets.

## 3

Divide each term in the original expression by the Greatest Common Factor.
## 1

Divide the 1## 2

Divide the 2

## 1^{st} Term

Divide the 1^{st}term (**2x**) in the original expression by the Greatest Common Factor (^{2}**2x**). Write this as the 1^{st}term inside the bracket.## 2^{nd} Term

Divide the 2^{nd}term (**2xy**) in the original expression by the Greatest Common Factor (**2x**). Write this as the 2^{nd}term inside the bracket, and add to the previous result.**Note:**The term is added because there is a**+**before the second term in the original expression.## Answer:

We have factored the expression.**Check**that the expression has been factored correctly by expanding the brackets to see if you get the original expression.

## Factoring, Factorising

The method is refered to as 'factoring' or 'factorising'. The verb is 'to factor' or 'to factorise'.## What Is the Greatest Common Factor in Algebra?

The greatest common factor in algebra is the largest factor that is common to two or more terms.## Expressions with More than Two Terms

Expressions can have more than two terms that are added or subtracted together. These expression are factored in the same way. The Greatest Common Factor must be found for**all**the terms in the expression.

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