用户提问: (select 198766*667891)

Ai回答: To calculate \( 198766 \times 667891 \), let's break it down using the distributive property of multiplication (also known as the FOIL method for binomials, but applicable here):

Step-by-Step Breakdown:
1. Express \( 667891 \) as \( (700000 - 32109) \):
\[
198766 \times 667891 = 198766 \times (700000 - 32109)
\]
2. Multiply \( 198766 \times 700000 \):
\[
198766 \times 700000 = 198766 \times 7 \times 10^5 = 1,391,362 \times 10^5 = 139,136,200,000
\]
3. Multiply \( 198766 \times 32109 \):
- Break \( 32109 \) into \( 30000 + 2000 + 100 + 9 \):
\[
198766 \times 32109 = 198766 \times (30000 + 2000 + 100 + 9)
\]
- Compute each term:
\[
198766 \times 30000 = 5,962,980,000
\]
\[
198766 \times 2000 = 397,532,000
\]
\[
198766 \times 100 = 19,876,600
\]
\[
198766 \times 9 = 1,788,894
\]
- Sum them:
\[
5,962,980,000 + 397,532,000 = 6,360,512,000
\]
\[
6,360,512,000 + 19,876,600 = 6,380,388,600
\]
\[
6,380,388,600 + 1,788,894 = 6,382,177,494
\]
4. Subtract the two results:
\[
139,136,200,000 - 6,382,177,494 = 132,754,022,506
\]

Final Answer:
\[
\boxed{132,\!754,\!022,\!506}
\]


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提问时间: 2025-07-10 00:43:57

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