Certainly! Let's find the product of [tex]\(3x\left(x^2 + 4\right)\)[/tex] step-by-step.
### Step 1: Understand the Expression
We are given the expression:
[tex]\[ 3x(x^2 + 4) \][/tex]
### Step 2: Apply the Distribution Property
Using the distributive property of multiplication over addition, we'll multiply [tex]\(3x\)[/tex] by each term inside the parentheses:
[tex]\[
3x \cdot x^2 + 3x \cdot 4
\][/tex]
### Step 3: Perform Multiplications
Let's do these multiplications one by one:
1. Multiply [tex]\(3x\)[/tex] by [tex]\(x^2\)[/tex]:
[tex]\[ 3x \cdot x^2 = 3x^3 \][/tex]
2. Multiply [tex]\(3x\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[ 3x \cdot 4 = 12x \][/tex]
### Step 4: Combine the Results
Now, we add these two results together:
[tex]\[
3x^3 + 12x
\][/tex]
### Conclusion
The product of [tex]\(3x(x^2 + 4)\)[/tex] is:
[tex]\[
3x^3 + 12x
\][/tex]
So, the correct option is:
[tex]\(\boxed{3x^3 + 12x}\)[/tex]
