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【347250】《同类项》基础练习

时间:2025-03-05 20:06:04 作者: 字数:3767字
简介:

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a>








6.2 同类项

1、什么叫做同类项?怎样合并同类项?



2、下列各题中的两个项是不是同类项?

(1)3x2y3x2y (2)0.2a2b0.2ab2(3)11abc9bc

(4)3m2n3n3m2(5)4xy2z4x2yz (6)62x2




3、下列各题合并同类项的结果对不对?不对的,指出错在哪里。

(1)3a+2b=5ab (2)5y22y2=3(3)4x2y5y2x=x2y

  1. a+a=2a (5)7ab7ba=0 (6)3x2+2x3=5x5




4、合并下列各式中的同类项:

(1)15x+4x10x (2)6ab+ba+8ab(3)p2p2p2

  1. mn2+mn2(5) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x3+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x3 (6) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x0.3y <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x+0.3y




5、求下列各式的值:

(1)3c28c+2c313c2+2c2c3+3,其中c=4

(2)3y46x3y4y4+2yx3其中x=2y=3




6、解方程

(1)3x52x=1 (2)  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> +4x+3=0




7、把(a+b)(xy)各当作一个因式合并下列各式中的同类项

(1)4(a+b)+2(a+b)7(a+b)(2)3(xy)27(xy)+8(xy)2+6(xy)





  1. 有这样一道题:a=0.35b=0.28时,求多项式7a36a3b+3a2b+3a3+6a3b3a2b10a3的值。有一位同学指出,题目中给出的条件a=0.35b=0.28是多余的,他的说法有没有道理?






9、解方程:

(1)4x+33x2=0 (2)12x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a>4x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> =0(3)3x2x=0(4)x+1x+1=0






参考答案

1(1)所含字母相同,并且相同字母的次数也相同的项叫做同类项,几个常数项也是同类项。

(2)同类项的系数相加,所得结果作为系数,字母和字母的指数不变。

(3)单项式和多项式统称整式。

2(1)是; (2)不是同类项,因为相同字母的指数不同;

(3)不是;因为字母不相同;(4)是;

(5)不是,因为x的指数不同,y的指数也不同;

(6)不是,因为字母不相同。

3(1)不对,因为3a2b不是同类项,不能合并;

(2)不对,因为合并同类项时,丢掉了字母及字母的指数y2

(3)不对,因为4x2y与-5y2x不是同类项,不能合并;

(4)对;(5)对;(6)不对,3x23x3不是同类项,不能合并。

4(1)9x (2)3ab (3)3p2 (4)2m2n2 (5) 0 (6) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x

5(1)3c28c+2c313c2+2c2c3+3

 =(313)c2+(8+2)c+(22)c3+3

  =10c26c+3

c=4时,原式=10×(4)26×(4)+3=160+24+3=133

(2)3y46x3y4y4+2yx3=(34)y4+(6+2)x3y=y44x3y

x=2y=3时;原式=344×(2)3×3=81+96=15

6(1)3x52x=1

  解:方程两边都加上5得:3x2x=6;合并同类项得:x=6

(2) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> +4x+3=0

解:合并同类项得: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> =0;方程两边都减去 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> 得: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> x= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a>

方程两边都乘以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> 得:x=1

7(1)4(a+b)+2(a+b)7(a+b)=(4+27)(a+b)=(a+b)

(2)3(xy)27(xy)+8(xy)2+6(xy)

 =(3+8)(xy)2+(7+6)(xy)=11(xy)2(xy)

8、解7a36a3b+3a2b+3a3+6a3b3a2b10a3

    =(7+310)a3+(6+6)a3b+(33)a2b

    =0

 无论ab取任何值,多项式的值都等于0

 这位同学的说法有道理。

9(1)4x+33x2=0

解:合并同类项:得:x+1=0;方程两边都减去1,得:x=1

(2)12x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a>4x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a> =0

解:合并同类项,得:8x1=0

 方程两边都加上1,得:8x=1;方程两边都除以8,得:x= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/197/" title="基础" class="c1" target="_blank">基础</a> <a href="/tags/831/" title="同类" class="c1" target="_blank">同类</a> <a href="/tags/861/" title="同类项" class="c1" target="_blank">同类项</a>

(3)3x2x=0

解:合并同类项,得:x=0

(4)x+1x+1=0

解:合并同类项,得:-2x+2=0

 方程两边都减去2,得:-2x=2;方程两边都除以-2,得:x=1.



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