Sure! Let's simplify the given expression step-by-step.
The expression to simplify is:
[tex]\[ 3(4x + 5) \][/tex]
### Step 1: Apply the Distributive Property
The distributive property states that [tex]\( a(b + c) = ab + ac \)[/tex]. Here, [tex]\( a = 3 \)[/tex], [tex]\( b = 4x \)[/tex], and [tex]\( c = 5 \)[/tex]. We'll distribute the 3 across the terms inside the parentheses.
### Step 2: Multiply 3 by Each Term Inside the Parentheses
1. Multiply 3 by [tex]\( 4x \)[/tex]:
[tex]\[ 3 \cdot 4x = 12x \][/tex]
2. Multiply 3 by 5:
[tex]\[ 3 \cdot 5 = 15 \][/tex]
### Step 3: Combine the Terms
Now, add the results from the multiplication:
[tex]\[ 12x + 15 \][/tex]
### Conclusion
The simplified form of the expression [tex]\( 3(4x + 5) \)[/tex] is:
[tex]\[ 12x + 15 \][/tex]
So, to fill in the blanks in your equation:
[tex]\[ 3(4x + 5) = 12x + 15 \][/tex]
Therefore,
[tex]\[ 3(4x + 5) = \boxed{12} x + \boxed{15} \][/tex]
