How to Factor an Expression
Factoring an Expression
Factoring is a way of simplifying an expression.
Factoring writes an expression as a product of 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, a is multiplying (b + c).
Factoring has been achieved by taking the 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.
StepbyStep:
1
Find the Greatest Common Factor of the terms in the expression.
The terms in the expression are 2x^{2} and 2xy.

Look at the number that appears in both terms.
2 x^{2}, 2 xy
Find the greatest common factor of these numbers. In our example, the greatest common factor of 2 and 2 is 2.
Read more about finding the Greatest Common Factor of a number

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^{1}), whereas x^{2} has an exponent of 2).

Write these terms next to each other.
2x is the Greatest Common Factor of 2x^{2} and 2xy.
Read 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^{st} Term
Divide the 1^{st} term (2x^{2}) in the original expression by the Greatest Common Factor (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.