The LessonFactoring 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 ExpressionFactoring 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).
How to Factor an ExpressionFactoring an expression is easy.
QuestionFactor the expression below.
Find the Greatest Common Factor of the terms in the expression. The terms in the expression are 2x2 and 2xy.
Look at the number that appears in both terms.
2 x2, 2 xyFind 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 x2 , 2 x yx has the smallest exponent. (x has an implicit exponent of 1 (x = x1), whereas x2 has an exponent of 2).
- Write these terms next to each other. 2x is the Greatest Common Factor of 2x2 and 2xy. Read more about finding the greatest common factor in algebra
Write the Greatest Common Factor outside of the brackets.
Divide each term in the original expression by the Greatest Common Factor.
1st TermDivide the 1st term (2x2) in the original expression by the Greatest Common Factor (2x). Write this as the 1st term inside the bracket.
2nd TermDivide the 2nd term (2xy) in the original expression by the Greatest Common Factor (2x). Write this as the 2nd 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.