问题 解答题

先分解因式(1)、(2)、(3),再解答后面问题;

(1)1+a+a(1+a);

(2)1+a+a(1+a)+a(1+a)2

(3)1+a+a(1+a)+a(1+a)2+a(1+a)3

问题:

a.先探索上述分解因式的规律,然后写出:1+a+a(1+a)+a(1+a)2+a(1+a)3+…+a(1+a)2007分解因式的结果是______.

b.请按上述方法分解因式:1+a+a(1+a)+a(1+a)2+a(1+a)3+…+a(1+a)n(n为正整数).

答案

(1)原式=(1+a)(1+a)=(1+a)2

(2)原式=(1+a)[1+a+a(1+a)]=(1+a)(1+a)(1+a)=(1+a)3

(3)原式=(1+a)[1+a+a(1+a)+a(1+a)2],

=(1+a)(1+a)[1+a+a(1+a)],

=(1+a)2(1+a)(1+a),

=(1+a)4

a.(1+a)2008

b.原式=(1+a)[1+a+a(1+a)+a(1+a)2+…+a(1+a)n-1],

=(1+a)(1+a)[1+a+a(1+a)+a(1+a)2+…+a(1+a)n-2],

=(1+a)2(1+a)[1+a+a(1+a)+a(1+a)2+…+a(1+a)n-3],

=(1+a)n-1(1+a)(1+a)=(1+a)n+1

翻译题

完成句子。

阅读下列各小题,根据每句后的汉语提示,用句末括号内的英语单词完成句子.

1.As time ____________________, I come to realize how much my life has been connected with my

interest in computers. (go)

随着时间的流逝,我开始意识到我的生活已经跟我对电脑的兴趣联系到了一起.

2.It will be updated in a short time before the software ____________________ the program. (apply)

在这个软件应用于程序之前,短期内将会被更新.

3.Medical researchers have painfully realized that there are many problems to __________________

any solution so far. (find)

医学研究者们已经痛苦地意识到,到目前为止仍然有许多问题找不到任何解决的办法.

4.The young man told of his adventures while __________________ the United States in 89 days.

(hike)

这个年轻人讲述了他徒步穿越美国的89天冒险之旅.

5.He went to the university and studied IT, ______________________a special interest in artificial

intelligence. (develop)

他进入大学学习信息技术,这使他对人工智能产生了特别的兴趣.

6.Kate is now wearing a satisfied look. She ____________ the speech successfully. (deliver)

此刻凯特一脸的满足,她的演进肯定成功了.

7.____________________ is that he constantly wishes to improve himself in terms of knowledge and

skills. (impress)

让我印象最深刻的是他一直希望自己在知识和技能方面能不断提高.

8.____________________ that we can download the exercises through the Internet. (occur)

我突然想到我们可以通过网络下载习题.

9.Our headteacher is easygoing, __________________ I have learned how to use the computer. (help)

我们的班主任很随和,在他的帮助下我学会了怎样使用电脑.

10.We've been told the good news, but when and where to go for the exciting vacation ____________________ yet. (decide)

我们得知了这则好消息,但是什么时间、去什么地方度过这个令人兴奋的假期尚未确定.

单项选择题