Answered

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Suppose you multiplied the cereal box dimensions in a different order:
[tex]\[ V = (x)(4x+3)(4x) \][/tex]

First, [tex]\((x)(4x+3) = \square\)[/tex]

[tex]\[
\begin{array}{l}
A. 7x \\
B. 7x^2 \\
C. 4x^2 + 3 \\
D. 4x^2 + 3x \\
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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.
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