Certainly! Let's factorize the expression [tex]\( 15(k+g)^2 - 20(k+g) \)[/tex] step by step.
### Step 1: Identify a common factor
Observe that both terms in the expression have a common factor of [tex]\( (k+g) \)[/tex]. We can factor this out.
[tex]\[ 15(k+g)^2 - 20(k+g) = (k+g) \cdot [15(k+g) - 20] \][/tex]
### Step 2: Simplify the remaining expression inside the brackets
Next, we need to simplify [tex]\( 15(k+g) - 20 \)[/tex].
First, distribute the 15 inside the parenthesis:
[tex]\[ 15(k+g) - 20 = 15k + 15g - 20 \][/tex]
### Step 3: Combine the factored term
Now, we place the simplified expression back with the factored-out term:
[tex]\[ 15(k+g)^2 - 20(k+g) = (k+g) \cdot (15k + 15g - 20) \][/tex]
### Step 4: Identify further common factors if possible
We notice there isn't any further simplification directly from here, but this can be re-written to match the given result:
[tex]\[ 15(k+g)^2 - 20(k+g) = 5(k+g) \cdot (3k + 3g - 4) \][/tex]
### Final Factorized Form
Thus, the factorized form of the given expression is:
[tex]\[ 5(k+g)(3k+3g-4) \][/tex]
So, the expression [tex]\( 15(k+g)^2 - 20(k+g) \)[/tex] factorizes to:
[tex]\[ 5 (k+g) ( 3k+3g-4) \][/tex]
This completes the factorization process.
