Sure, let’s factor the expression [tex]\(5ab(x + 6) - 4(x + 6)\)[/tex] completely, step-by-step.
### Step 1: Identify the common factor
First, notice that both terms [tex]\(5ab(x + 6)\)[/tex] and [tex]\(-4(x + 6)\)[/tex] have a common factor: [tex]\((x + 6)\)[/tex].
### Step 2: Factor out the common term
We can factor out [tex]\((x + 6)\)[/tex] from each term in the expression:
[tex]\[ 5ab(x + 6) - 4(x + 6) \][/tex]
When you factor out [tex]\((x + 6)\)[/tex], you effectively remove it from each term:
[tex]\[ (x + 6)(5ab) - (x + 6)(4) \][/tex]
### Step 3: Simplify the expression inside the parentheses
Now, combine the terms inside the parentheses:
[tex]\[ (x + 6) [5ab - 4] \][/tex]
The expression inside the parentheses is now simplified to [tex]\(5ab - 4\)[/tex].
### Final Step: Write the completely factored expression
Therefore, the completely factored form of the given expression is:
[tex]\[ (x + 6)(5ab - 4) \][/tex]
### Conclusion
The fully factored form of [tex]\(5ab(x + 6) - 4(x + 6)\)[/tex] is:
[tex]\[ \boxed{(x + 6)(5ab - 4)} \][/tex]
