2007×20082008-2008×20072007= ．

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

1. 将大数进行拆分，显现其数位特征及公共因子

根据数位特征，可以将含有重复数字的多位数进行拆分：
$20082008 = 2008 \times 10001$
$20072007 = 2007 \times 10001$

2. 利用乘法交换律与结合律化简计算并求值

代入原式得：

\begin{aligned} & 2007 \times 20082008 - 2008 \times 20072007 \\ &= 2007 \times 2008 \times 10001 - 2008 \times 2007 \times 10001 \end{aligned}

根据乘法交换律，有 $2007 \times 2008 = 2008 \times 2007$ ，
因此，两项相等，相减结果为 $0$ 。

Answer

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.