Sure, I'll provide you with a detailed step-by-step solution.
Let's address the expression step by step.
1. First, we are given the expression:
[tex]\[
V = (x)(4x + 3)(4x)
\][/tex]
2. First step: Let's multiply [tex]\(x\)[/tex] by [tex]\((4x + 3)\)[/tex]:
[tex]\[
x \cdot (4x + 3) = 4x^2 + 3x
\][/tex]
So, we have:
[tex]\[
(x)(4x + 3) = 4x^2 + 3x
\][/tex]
3. Next step: Multiply the resulting expression by [tex]\(4x\)[/tex]:
[tex]\[
(4x^2 + 3x) \cdot 4x
\][/tex]
4. Distribute [tex]\(4x\)[/tex] to every term inside the parenthesis:
[tex]\[
4x \cdot 4x^2 + 4x \cdot 3x
\][/tex]
5. Perform the multiplications:
[tex]\[
4x \cdot 4x^2 = 16x^3
\][/tex]
[tex]\[
4x \cdot 3x = 12x^2
\][/tex]
6. Combine these results:
[tex]\[
V = 16x^3 + 12x^2
\][/tex]
Therefore, the expression for the volume after multiplying the terms is:
[tex]\[
V = 16x^3 + 12x^2
\][/tex]
