合并同类项练习题and有理数混合运算练习题

1个回答

  • 例1、合并同类项

    (1)(3x-5y)-(6x+7y)+(9x-2y)

    (2)2a-[3b-5a-(3a-5b)]

    (3)(6m2n-5mn2)-6(m2n-mn2)

    (1)(3x-5y)-(6x+7y)+(9x-2y)

    =3x-5y-6x-7y+9x-2y (正确去掉括号)

    =(3-6+9)x+(-5-7-2)y (合并同类项)

    =6x-14y

    (2)2a-[3b-5a-(3a-5b)] (应按小括号,中括号,大括号的顺序逐层去括号)

    =2a-[3b-5a-3a+5b] (先去小括号)

    =2a-[-8a+8b] (及时合并同类项)

    =2a+8a-8b (去中括号)

    =10a-8b

    (3)(6m2n-5mn2)-6(m2n-mn2) (注意第二个括号前有因数6)

    =6m2n-5mn2-2m2n+3mn2 (去括号与分配律同时进行)

    =(6-2)m2n+(-5+3)mn2 (合并同类项)

    =4m2n-2mn2

    例2.已知:A=3x2-4xy+2y2,B=x2+2xy-5y2

    求:(1)A+B (2)A-B (3)若2A-B+C=0,求C.

    (1)A+B=(3x2-4xy+2y2)+(x2+2xy-5y2)

    =3x2-4xy+2y2+x2+2xy-5y2(去括号)

    =(3+1)x2+(-4+2)xy+(2-5)y2(合并同类项)

    =4x2-2xy-3y2(按x的降幂排列)

    (2)A-B=(3x2-4xy+2y2)-(x2+2xy-5y2)

    =3x2-4xy+2y2-x2-2xy+5y2 (去括号)

    =(3-1)x2+(-4-2)xy+(2+5)y2 (合并同类项)

    =2x2-6xy+7y2 (按x的降幂排列)

    (3)∵2A-B+C=0

    ∴C=-2A+B

    =-2(3x2-4xy+2y2)+(x2+2xy-5y2)

    =-6x2+8xy-4y2+x2+2xy-5y2 (去括号,注意使用分配律)

    =(-6+1)x2+(8+2)xy+(-4-5)y2 (合并同类项)

    =-5x2+10xy-9y2 (按x的降幂排列)

    例3.计算:

    (1)m2+(-mn)-n2+(-m2)-(-0.5n2)

    (2)2(4an+2-an)-3an+(an+1-2an+1)-(8an+2+3an)

    (3)化简:(x-y)2-(x-y)2-[(x-y)2-(x-y)2]

    (1)m2+(-mn)-n2+(-m2)-(-0.5n2)

    =m2-mn-n2-m2+n2 (去括号)

    =(-)m2-mn+(-+)n2 (合并同类项)

    =-m2-mn-n2 (按m的降幂排列)

    (2)2(4an+2-an)-3an+(an+1-2an+1)-(8an+2+3an)

    =8an+2-2an-3an-an+1-8an+2-3an (去括号)

    =0+(-2-3-3)an-an+1 (合并同类项)

    =-an+1-8an

    (3)(x-y)2-(x-y)2-[(x-y)2-(x-y)2] [把(x-y)2看作一个整体]

    =(x-y)2-(x-y)2-(x-y)2+(x-y)2 (去掉中括号)

    =(1--+)(x-y)2 (“合并同类项”)

    =(x-y)2

    例4求3x2-2{x-5[x-3(x-2x2)-3(x2-2x)]-(x-1)}的值,其中x=2.

    分析:由于已知所给的式子比较复杂,一般情况都应先化简整式,然后再代入所给数值x=-2,去括号时要注意符号,并且及时合并同类项,使运算简便.

    原式=3x2-2{x-5[x-3x+6x2-3x2+6x]-x+1} (去小括号)

    =3x2-2{x-5[3x2+4x]-x+1} (及时合并同类项)

    =3x2-2{x-15x2-20x-x+1} (去中括号)

    =3x2-2{-15x2-20x+1} (化简大括号里的式子)

    =3x2+30x2+40x-2 (去掉大括号)

    =33x2+40x-2

    当x=-2时,原式=33×(-2)2+40×(-2)-2=132-80-2=50

    例5.若16x3m-1y5和-x5y2n+1是同类项,求3m+2n的值.

    ∵16x3m-1y5和-x5y2n+1是同类项

    ∴对应x,y的次数应分别相等

    ∴3m-1=5且2n+1=5

    ∴m=2且n=2

    ∴3m+2n=6+4=10

    本题考察我们对同类项的概念的理解.

    例6.已知x+y=6,xy=-4,求: (5x-4y-3xy)-(8x-y+2xy)的值.

    (5x-4y-3xy)-(8x-y+2xy)

    =5x-4y-3xy-8x+y-2xy

    =-3x-3y-5xy

    =-3(x+y)-5xy

    ∵x+y=6,xy=-4

    ∴原式=-3×6-5×(-4)=-18+20=2

    说明:本题化简后,发现结果可以写成-3(x+y)-5xy的形式,因而可以把x+y,xy的值代入原式即可求得最后结果,而没有必要求出x,y的值,这种思考问题的思想方法叫做整体代换,希望同学们在学习过程中,注意使用.

    三、练习

    (一)计算:

    (1)a-(a-3b+4c)+3(-c+2b)

    (2)(3x2-2xy+7)-(-4x2+5xy+6)

    (3)2x2-{-3x+6+[4x2-(2x2-3x+2)]}

    (二)化简

    (1)a>0,