In the Math Essential Parentheses, you learned that
and that
But how do you simplify an expression like into ? Let’s look at calculations in the reverse order of what we’ve been reviewing up to now.
If you’ve got an expression you’d like to factorize, you can just use the following method:
Rule
You’ll be able to best learn this process through an example:
Example 1
Only Numbers
Factorize the expression
If you follow the method above, you have and . Therefore
Here 2 is a common factor that you can put outside of the parentheses, and you therefore have to remove a 2 from each term inside the parentheses:
You should check that the two expressions give the same answer. The left-hand side is , and the right-hand side is . Since these are equal, you know that the factorization is correct.
Factorization has a surprising number of applications, and here you’ll look at a few of them.
Often, you’ll have to put several factors outside the parentheses. Here’s an example:
Example 2
Algebraic Expressions
Factorize the expression
Factorizing each term gives
The common factors for all terms are 3 and , meaning that you get
This gives you the following rule:
Rule
Here is an example with powers:
Example 3
Factorize
By factoring each term separately, you see that 3 and are common factors for all terms (try yourself).
Therefore the expression becomes