Factoring Expressions (Mathematics Lesson)
Factoring Expressions
Factoring is a way of simplifying an expression into factors.
Imagine we wanted to factor the expression below. We would take out a common factor from each term outside of a bracket, leaving another expression inside the bracket.
It is the opposite of expanding brackets.
Understanding Factoring an Expression
Factoring allows us to change an expression where terms are added (or subtracted) together to one where they are multiplied together.

On the lefthand side of the equation, ab and ac are added together.

On the righthand side of the equation, the a term, which is common to ab and ac, has been taken outside of a bracket. This leaves b + c inside the bracket.
a is multiplying (b + c). They are factors of a product.
How to Factor an Expression
Fac Question: Factor the expression below.Step 1
The terms in the expression are 2x^{2} and 2xy.
The Greatest Common Factor is 2x:
Step 2
Step 3
1^{st} term
Divide the 1^{st} term in the expression by the Greatest Common Factor.
This becomes the 1^{st} term inside the bracket.
2^{nd} term
Divide the 2^{nd} term in the expression by the Greatest Common Factor.
This becomes the 2^{nd} term inside the bracket.
The expression has been factored.
Note: To check that the expression has been factored correctly, expand the bracket to see if the original expression is obtained.
A Real Example of How to Factor an Expression
The slider below shows a real example of how to factor an expression.How to Factor an Expression into Two Brackets
Quadratic equations can be factored into two brackets.A quadratic equation can be solved using factoring.
Read more about how to solve quadratic equations using factoring
How to Factor a Difference of Squares
The difference of squares is a special type of quadratic equation:A difference of squares always factors to a simple expression:
Read more about how to factor a difference of squares
Curriculum
Interactive Test
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FACTORING & FACTORISING, TO FACTOR & TO FACTORISEThis method has slightly different terms depending on which country you are from.
In American English, the method is factoring and the verb is 'to factor'.
In British English, the method is factorising and the verb is 'to factorise'.
WHAT IS THE GREATEST COMMON FACTOR IN ALGEBRA?
The Greatest Common Factor 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 found in Step 1 must be found for all the terms in the expression.