问题 解答题

你能化简(x-1)(x99+x98+x97+……+x+1)吗?遇到这样的问题,我们可以先思考一下,从简单的情形入手.

分别计算下列各式的值:

①(x-1)(x+1)=x2-1;

②(x-1)(x2+x+1)=x3-1;;

③(x-1)(x3+x2+1)=x4-1;;……

由此我们可以得到:(x-1)(x99+x98+x97+…+x+1)=________________;

请你利用上面的结论,完成下面两题的计算:

(1) 299+298+297+……+2+1;

(2)(-2)50+(-2)49+(-2)48+……+(-2)+1

答案

2100-1;(1)2100-1;(2).

题目分析:根据平方差公式,和立方差公式可得前2个式子的结果,利用多项式乘以多项式的方法可得出第3个式子的结果;从而总结出规律是(x-1)(x99+x98+x97+…+x+1)=x100-1,根据上述结论计算下列式子即可.

试题解析:根据题意:(1)(x-1)(x+1)=x2-1;

(2)(x-1)(x2+x+1)=x3-1;

(3)(x-1)(x3+x2+x+1)=x4-1;

故(x-1)(x99+x98+x97+…+x+1)=x100-1.

根据以上分析:

(1)299+298+297+…+2+1=(2-1)(299+298+297+…+2+1)=2100-1;

(2)(-2)50+(-2)49+(-2)48+…(-2)+1=-(-2-1)[(-2)50+(-2)49+(-2)48+…(-2)+1]

=-(-251-1)=.

阅读理解

阅读理解。

     Nancy and her family moved into a new house with a big garden. She didn't have many friends in her new

neighborhood, so after she sent her husband and children to work and school, she spent a lot of time in the

garden. She loved the flowers, shrubs (灌木) and trees.

     One day, when Nancy was expecting some special visitors, she took extra care of the garden. She pulled

the weeds, trimmed (修剪) the shrubs, cut the grass, and carefully cleaned all the dry autumn leaves. As she

was working, an old woman was watching her with interest over the fence. Nancy had met this woman several

times in the streets. She seemed to be friendly to everybody.

     When Nancy had finished, she stood back to admire her work. "Isn't it beautiful?" she called out to the old

woman. "Yes," replied the old woman, "but there is something missing. May I come in? I'll put it right for you." 

     Nancy opened the gate for her and let her in. slowly, the old woman walked to the tree near the center of

the garden, held it by the trunk, and shook it. Leaves showered down all over the garden. "Now," said the old

woman, "isn't it much better?"

     Nancy looked at her garden for a while and said, "Strange. The leaves make the garden look more beautiful?" 

     The old woman smiled and said, "When you are as old as me, you'll understand life can't be perfect. The

fallen leaves are part of nature's beauty."

1. Why did Nancy spend most of her time around her house? [ ]

A. She was very busy with her work.

B. She had to take care of her children.

C. She thought the neighborhood unsafe.

D. She had few friends in the neighborhood.

2. What did Nancy do in the garden before the visitors came? [ ]

A. She picked some flowers in the garden.

B. She invited a neighbor to give her advice.

C. She moved tables and chairs into the garden.

D. She tried to make the garden tidy and beautiful.

3. From the text, we can learn that the old woman was _____. [ ]

A. rich and energetic

B. wise and friendly

C. quiet and sensitive

D. lively and humorous

4. What would be the best title of the text? [ ]

A. Nature's beauty

B. An autumn story

C. The art of garden

D. A happy housewife

单项选择题