Absolutely, let’s solve the problem step-by-step.
We are given the expression [tex]\( V = (x)(4x + 3)(4x) \)[/tex].
First, let’s simplify the expression by multiplying [tex]\( x \)[/tex] with [tex]\( 4x + 3 \)[/tex].
#### Step 1:
Multiply [tex]\( x \)[/tex] and [tex]\( 4x + 3 \)[/tex]:
[tex]\[ (x)(4x + 3) \][/tex]
To do this, distribute [tex]\( x \)[/tex]:
[tex]\[ x \cdot 4x + x \cdot 3 \][/tex]
This simplifies to:
[tex]\[ 4x^2 + 3x \][/tex]
So, [tex]\( (x)(4x + 3) = 4x^2 + 3x \)[/tex].
#### Step 2:
Now we need to multiply [tex]\( (4x^2 + 3x) \)[/tex] by [tex]\( 4x \)[/tex]:
[tex]\[ (4x^2 + 3x) \cdot 4x \][/tex]
Distribute [tex]\( 4x \)[/tex]:
[tex]\[ 4x^2 \cdot 4x + 3x \cdot 4x \][/tex]
This simplifies to:
[tex]\[ 16x^3 + 12x^2 \][/tex]
So, the final result of [tex]\( (x)(4x + 3)(4x) \)[/tex] is:
[tex]\[ 16x^3 + 12x^2 \][/tex]
So the volume [tex]\( V \)[/tex] can be expressed as:
[tex]\[ V = 16x^3 + 12x^2 \][/tex]
And that’s the detailed step-by-step solution to the problem.
