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.
