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【329977】14.1.4单项式与多项式相乘

时间:2025-02-07 09:15:20 作者: 字数:2122字

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

14.1.4 单项式与多项式相乘

随堂检测

1、单项式和单项式相乘,把它们的 分别相乘,对于只在一个单项式中出现的字母,则连同它的指数一起积得一个

2、单项式和多项式相乘,用单项式去乘多项式的 ,再把所得的积

3、化简: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> 的结果是

A <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> B <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> C <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> D <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

4、下列运算正确的是( )

A2 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> + <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> =3 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> B2 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> =1 C2 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> · <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> =3 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> D2 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> ÷ <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> = <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

5、化简: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

典例分析

例题:计算: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

分析;单项式乘法运算是以幂的运算为基础,计算时应注意①先进行系数运算;②按运算顺序进行;③凡是在单项式中出现的字母,在结果中也应全有,不能漏项;④注意符号;⑤合并同类项的结果按某字母的降幂排列。

解: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

课下作业

拓展提高

1、若 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> ,则 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> 的值是_______________

2、卫星绕地球的运转速度为 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> ,求卫星绕地球运转 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> 的运行路程



3、解方程: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>





4、先化简,再求值: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> ,其中 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>





5、先化简,再求值: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> ,其中 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>




体验中考

1、(江苏)若 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> ,则 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

2(浙江嘉兴)下列运算正确的是(  )

A <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> B <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

C <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> D <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

3、(湖南衡阳)已知 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> ,则 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> 的值是(

A0 B2 C5 D8

4、(广西贺州)计算: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> =





























参考答案

随堂检测

1、系数,相同字母,因式

2、每一项,相加

3A  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

4A

5、解: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> = <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

课下作业

拓展提高

12009

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> 代入,得 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

2、解: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

3、解: <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

4 解:原式= <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

= <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> 时,原式= <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> = <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  

5 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

所以当x= <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> 时,原式=4

体验中考

11  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> = <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

2D

3D  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>

4 <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>  <a href="/tags/877/" title="单项式" class="c1" target="_blank">单项式</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a>