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.
