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Complete the standard multiplication algorithm for [tex]$432 \times 958$[/tex], including any "carried," or regrouped digits, if necessary.

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To find the product of [tex]\(432 \times 958\)[/tex] using the standard multiplication algorithm, we follow these steps:

1. Multiply each digit of 432 by the units digit of 958 (which is 8):

[tex]\[ \begin{array}{ccc} & 432 & \times 8 \\ \hline & 3456 & \\ \end{array} \][/tex]

Here, [tex]\(432 \times 8 = 3456\)[/tex].

2. Multiply each digit of 432 by the tens digit of 958 (which is 5), and then multiply by 10:

[tex]\[ \begin{array}{ccc} & 432 & \times 50 \\ \hline & 21600 & \\ \end{array} \][/tex]

Here, [tex]\(432 \times 5 = 2160\)[/tex], and multiplying by 10 gives [tex]\(21600\)[/tex].

3. Multiply each digit of 432 by the hundreds digit of 958 (which is 9), and then multiply by 100:

[tex]\[ \begin{array}{ccc} & 432 & \times 900 \\ \hline & 388800 & \\ \end{array} \][/tex]

Here, [tex]\(432 \times 9 = 3888\)[/tex], and multiplying by 100 gives [tex]\(388800\)[/tex].

4. Add the results of each step:

[tex]\[ \begin{array}{r} 3456 \\ 21600 \\ 388800 \\ \hline 413856 \\ \end{array} \][/tex]

The final product of [tex]\(432 \times 958\)[/tex] is [tex]\(413856\)[/tex].

This completes the standard multiplication algorithm, demonstrating the step-by-step multiplication, including the handling and summing of intermediate results.
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