Sure, let's go through the process of factoring the given expression step by step.
Given expression:
[tex]\[ 27x^3 - 9x^2 \][/tex]
### Step 1: Factor out the greatest common factor (GCF)
First, identify the greatest common factor of the terms in the expression. Both terms have a common factor of [tex]\( 9x^2 \)[/tex].
[tex]\[ 27x^3 - 9x^2 = 9x^2(3x^1) - 9x^2(1) \][/tex]
So, we can factor out [tex]\( 9x^2 \)[/tex] from each term:
[tex]\[ 9x^2(3x) - 9x^2(1) = 9x^2(3x - 1) \][/tex]
### Step 2: Simplify the expression
The expression is now factored completely as:
[tex]\[ 9x^2(3x - 1) \][/tex]
### Final Factored Form
Therefore, the completely factored form of the expression [tex]\( 27x^3 - 9x^2 \)[/tex] is:
[tex]\[ 9x^2(3x - 1) \][/tex]
This concludes the factorization process.
