Factoring an Expression
(KS3, Year 7)
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).
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 2x2 and 2xy.
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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. finding the Greatest Common Factor of a number
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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. 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.
1st Term
Divide the 1st term (2x2) in the original expression by the Greatest Common Factor (2x). Write this as the 1st term inside the bracket.2nd Term
Divide 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.
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.Worksheet
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