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Match the multiplication problem on the left with the simplified polynomial.

[tex]\[
\begin{tabular}{ll}
$4 x\left(4 x^2 - x + 3\right)$ & \\
$(8 x + 1)(2 x - 3)$ & \\
$4 x^2(4 x)$ & \\
$(2 x + 3)\left(8 x^2 - 4 x + 3\right)$ & \\
\end{tabular}
\][/tex]

Options:

A. [tex]$16 x^2$[/tex]
B. [tex]$16 x^2 - 2$[/tex]
C. [tex]$16 x^3$[/tex]
D. [tex]$16 x^3 - 4$[/tex]
E. [tex]$16 x^3 + 1$[/tex]



Answer :

GinnyAnswer
To match the multiplication problems with their corresponding simplified polynomials, we need to carefully compare each problem on the left with each solution option on the right. Here's the detailed solution:

1. Consider the first multiplication problem: [tex]\( 4x(4x^2 - x + 3) \)[/tex].
- The correct simplified polynomial for this is found by matching:
[tex]\[ 4x(4x^2 - x + 3) = 16x + 3x. \][/tex]
- Therefore, [tex]\( 4x(4x^2 - x + 3) \)[/tex] matches with [tex]\( 16x + 3x \)[/tex].

2. For the second multiplication problem: [tex]\( (8x + 1)(2x - 3) \)[/tex].
- By comparing options, the simplified polynomial is:
[tex]\[ (8x + 1)(2x - 3) = 16x^2 - 2. \][/tex]
- Thus, [tex]\( (8x + 1)(2x - 3) \)[/tex] matches with [tex]\( 16x^2 - 2 \)[/tex].

3. Now look at the third multiplication problem: [tex]\( 4x^2(4x) \)[/tex].
- The correct match is:
[tex]\[ 4x^2(4x) = 16x^3. \][/tex]
- Hence, [tex]\( 4x^2(4x) \)[/tex] matches with [tex]\( 16x^3 \)[/tex].

4. Finally, for the fourth multiplication problem: [tex]\( (2x + 3)(8x^2 - 4x + 3) \)[/tex].
- The corresponding simplified polynomial is:
[tex]\[ (2x + 3)(8x^2 - 4x + 3) = 16x^3 - 4. \][/tex]
- So, [tex]\( (2x + 3)(8x^2 - 4x + 3) \)[/tex] matches with [tex]\( 16x^3 - 4 \)[/tex].

To summarize:

[tex]\[ \begin{array}{ll} 4x(4x^2 - x + 3) & 16x + 3x \\ (8x + 1)(2x - 3) & 16x^2 - 2 \\ 4x^2(4x) & 16x^3 \\ (2x + 3)(8x^2 - 4x + 3) & 16x^3 - 4 \\ \end{array} \][/tex]

This is the correct matching for each multiplication problem with its corresponding simplified polynomial.

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