整式的混合运算专项练习99题有答案有过程.docx
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整式的混合运算专项练习99题有答案有过程.docx
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整式的混合运算专项练习99题有答案有过程
整式的混合运算专项练习99题(有答案)
(1)﹣(2x2y3)²•(xy)3
(2)5x2(x+1)(x﹣1)
(3)x(y﹣x)+(x+y)(x﹣y);
(4)(a+2b)2+4ab3÷(﹣ab).
(5)3(a2)3•(a3)2﹣(﹣a)2(a5)2
(6)(5mn﹣2m+3n)+(﹣7m﹣7mn)
(7)(x+2)2﹣(x+1)(x﹣1)
(8)(x+2)2﹣(2x)2;
(9)(2a+3b)2﹣4a(a+3b+1).
(10)(﹣2xy2)2•3x2y÷(﹣x3y4)
(11)(x+1)2+2(1﹣x)
(12)(﹣a3)2•(﹣a2)3;
(13)[(﹣a)(﹣b)2•a2b3c]2;
(14)
;
(15)(x3)2÷x2÷x+x3÷(﹣x)2•(﹣x2).
(16)(﹣3x2)3•(﹣4y3)2÷(6x2y)3;
(17)(﹣x﹣y)2﹣(2y﹣x)(x+2y)
(18)
(19)(a+b)(﹣b+a)+(a+b)2﹣2a(a+b)
(20)
;
(21)x(x+1)﹣(2x+1)(2x﹣3);
(22)(2a+3b)2﹣(2a﹣3b)2.
(23)2a2﹣a8÷a6;
(24)(2﹣x)(2+x)+(x+4)(x﹣1)
(25)(﹣2ab3)2+ab4•(﹣3ab2);
(26)(2a+3)(2a﹣3)+(a﹣3)2.
(27)12ab2(abc)4÷(﹣3a2b3c)÷[2(abc)3].
(28)(﹣2x2)3÷(﹣x)2
(29)(﹣2m﹣1)(3m﹣2)
(30)2x•(﹣x2+3x)﹣3x2•(x+1).
(31)3a•(﹣ab2)﹣(﹣3ab)2.
(32)﹣3x•(2x2﹣x+4)
(33)2x3•(﹣2xy)(﹣
xy)3.
(34)3(x2﹣2x+3)﹣3x(x+1)=0.
(35)(3x+2)(3x+1)﹣(3x+1)2.
(36)2a(a+b)﹣(a+b)2.
(37)x(2x﹣7)+(3﹣2x)2.
(38)(﹣3x2y)2÷(﹣3x3y2)
(39)(a+2)2﹣(a+1)(a﹣1)
(40)(a2)4÷a2
(41)
.
(42)a(ab2﹣4b)+4a3b÷a2;
(43)(x﹣8y)(x﹣y).
(44)(3x2y)3•(﹣5y);
(45)[(x+y)2﹣y(2x+y)﹣4x]÷2x.
(46)(2x+a)2﹣(2x﹣a)2
(47)[(2x2)3﹣6x3(x3+2x2)]÷(﹣2x2)
(48)(x﹣2)(x+2)﹣(x+1)(x﹣3)
(49)(2a)3•b4÷12a3b2
(50)(3x﹣1)(2x+3)﹣6x2.
(51)(﹣6x2)2+(﹣3x2)•x﹣27x5÷(﹣9x2)
(52)(﹣2y2)3+y•y5
(53)(x+2)2﹣(x+1)(x﹣1)
(54)(a+b)(a﹣b)+(a+b)2﹣a(2a+b)
(55)(﹣a)2•(a2)2÷a3
(56)(15x2y﹣10xy2)÷5xy.
(57)[(2x2)3﹣6x3(x3+2x2+x)]÷(﹣x)4.
(58)(x+1)2+2(1﹣x)﹣x2
(59)(12a3﹣6a2+3a)÷3a
(60)5x2(x+1)(x﹣1)
(61)(b﹣2a)2﹣4a(a﹣b)
(62)(﹣3ab2)3(﹣4ab2)
(63)(3a﹣2)(a﹣6)
(64)(3a3b﹣9a2b2﹣21a2b3)÷(﹣3a2b)
(65)(x+3)(x﹣2)﹣(x﹣2)2
(66)(3x+4y)(3x﹣4y)
(67)(x+3y)(2x﹣y)﹣y(5x+3y)
(68)3(a5)2•(﹣a3)2﹣(2a3)2•(a2)5;
(69)4xy+(x﹣2y)2+(x+3y)(3y﹣x)
(70)﹣3x2y2•(﹣2xy)2.
(71)(a﹣2b)2+(a+2b)(a﹣2b)
(72)
.
(73)
.
(74)(﹣2xy2)3+(﹣3xy4)(﹣2x2y2)
(75)(2x)3×(﹣3xy2)
(76)(a+3b)(a﹣2b)﹣(2a﹣b)2.
(77)(﹣2x2y)3+(3x2)2•(﹣x2)•y3.
(78)(m2n)3•(﹣m4n)÷(﹣mn)2
(79)(2a﹣1)2(2a+1)2
(80)(x4y+6x3y2﹣x2y3)÷(3x2y)
(81)(2x﹣3y+1)(2x+3y﹣1)
(82)(﹣2x)(4x2﹣2x+1)
(83)(6a3﹣4a2+2a)÷2a
(84)(2x﹣y)(2x+y)﹣(x﹣3y)2
(85)(4x2﹣2x3+6x)÷(﹣2x)﹣(2x﹣1)2.
(86)
.
(87)[x(xy2+2xy)﹣y(x2y﹣6x2y2)]÷2x2y.
(88)x6÷(﹣x)2﹣(
x)2•27x2.
(89)(2x+y)(2x﹣3y)+4y(2x+y)
(90)(m+2)(m﹣2)+(m﹣1)(m+5)
(91)[(x+y)2﹣y(2x+y)﹣8x]÷2x.
(92)(2xy2﹣6xy)÷2x+y(y+2)
(93)(27a3﹣15a2+6a)÷(3a)
(94)x(x+2y)﹣(x+1)2+2x.
(95)
(x2y3)2÷(
x3y4)•(﹣4xy)
(96)a3•a3+(﹣2a3)2﹣(﹣a2)3.
(97)(2x+1)(x+3)﹣6(x2+x﹣1);
(98)[x(x2y2﹣xy)﹣y(x2﹣x3y)]+3x2y.
(99)[(2x+y)2﹣y(y+2x)﹣4x]÷2x.
整式混合运算99题参考答案:
(1)﹣(2x2y3)²•(xy)3
=﹣4x4y6•x3y3
=﹣4x7y9;
(2)5x2(x+1)(x﹣1),
=5x2(x2﹣1),
=5x4﹣5x2.
(3)x(y﹣x)+(x+y)(x﹣y),
=xy﹣x2+x2﹣y2,
=xy﹣y2;
(4)(a+2b)2+4ab3÷(﹣ab),
=a2+4ab+4b2﹣4b2,
=a2+4ab
(5)3(a2)3•(a3)2﹣(﹣a)2(a5)2,
=3a6•a6﹣a2•a10,
=3a12﹣a12,
=2a12.
(6)(5mn﹣2m+3n)+(﹣7m﹣7mn),
=5mn﹣2m+3n﹣7m﹣7mn,
=(5﹣7)mn+(﹣2+7)m+3n,
=3n﹣9m﹣2mn;
(7)(x+2)2﹣(x+1)(x﹣1),
=x2+4x+4﹣x2+x﹣x+1,
=4x+5.
(8)(x+2)2﹣(2x)2,
=x2+4x+4﹣4x2,
=﹣3x2+4x+4;
(9)(2a+3b)2﹣4a(a+3b+1),
=4a2+12ab+9b2﹣4a2﹣12ab﹣4a,
=9b2﹣4a.
(10)(﹣2xy2)2•3x2y÷(﹣x3y4),
=4x2y4•3x2y÷(﹣x3y4),
=12x4y5÷(﹣x3y4),
=﹣12xy
(11)(x+1)2+2(1﹣x),
=(x+1)2+2(1﹣x),
=x2+2x+1+2﹣2x,
=x2+3.
(12)(﹣a3)2•(﹣a2)3,
=a6•(﹣a6),
=﹣a12;
(13)[(﹣a)(﹣b)2•a2b3c]2,
=(﹣a3b5c)2,
=a6b10c2;
(14)
,
=(9×
×
)3,
=23,
=8;
(15)(x3)2÷x2÷x+x3÷(﹣x)2•(﹣x2),
=x6÷x2÷x+x3÷x2•(﹣x2),
=x3﹣x3,
=0.
(16)原式=﹣27x6•(16y6)÷(216x6y3)=﹣2y3;
(17)原式=(﹣x﹣y)2﹣(2y﹣x)(x+2y),
=x2+2xy+y2﹣(4y2﹣x2),
=x2+2xy+y2﹣4y2+x2,
=2xy﹣3y2
(18)
=[3x2y÷(﹣
xy)]+[﹣xy2÷(﹣
xy)]+[
xy÷(﹣
xy)],
=﹣6x+2y﹣1;
(19)(a+b)(﹣b+a)+(a+b)2﹣2a(a+b),
=(a+b)(a﹣b+a+b﹣2a),
=0
(20)原式=[2x(3x6y6)•
y2]÷9x7y8,
=(6x7y6•
y2)÷9x7y8,
=2x7y8÷9x7y8,
=
;
(21)原式=x2+x﹣(4x2﹣6x+2x﹣3),
=x2+x﹣4x2+6x﹣2x+3,
=﹣3x2+5x+3;
(22)原式=(2a+3b+2a﹣3b)(2a+3b﹣2a+3b),
=4a•9b,
=36ab
(23)2a2﹣a8÷a6,
=2a2﹣a2,
=a2;
(24)(2﹣x)(2+x)+(x+4)(x﹣1),
=4﹣x2+x2+3x﹣4,
=3x.
(25)(﹣2ab3)2+ab4•(﹣3ab2),
=4a2b6﹣3a2b6,
=a2b6;
(26)(2a+3)(2a﹣3)+(a﹣3)2,
=4a2﹣9+a2﹣6a+9,
=5a2﹣6a
(27)原式=12a5b6c4÷(﹣3a2b3c)÷2a3b3c3
=﹣4a3b3c3÷2a3b3c3=﹣2
(28)原式=﹣8x6÷x2=﹣8x4;
(29)原式=﹣6m2+4m﹣3m+2=﹣6m2+m+2
(30)原式=﹣2x3+6x2﹣3x3﹣3x2
=﹣5x3+3x2.
(31)3a•(﹣ab2)﹣(﹣3ab)2﹣12a2b2,
=﹣3a2b2﹣9a2b2﹣12a2b2,
=﹣24a2b2
(32)原式=﹣6x3+3x2﹣12x;
(33)原式=2x3•(﹣2xy)(﹣
x3y3)
=
x7y4
(34)3(x2﹣2x+3)﹣3x(x+1)=0,
∴3x2﹣6x+9﹣3x2﹣3x=0,
∴﹣9x=﹣9,
∴x=1
(35)原式=9x2+3x+6x+2﹣9x2﹣6x﹣1
=3x﹣1.
(36)2a(a+b)﹣(a+b)2.
=(a+b)(2a﹣a﹣b)
=(a+b)(a﹣b)
(37).原式=2x2﹣7x+9﹣12x+4x2
=6x2﹣19x+9.
(38)(﹣3x2y)2÷(﹣3x3y2),
=9x4y2÷(﹣3x3y2),
=﹣3x;
(39)(a+2)2﹣(a+1)(a﹣1),
=a2+4a+4﹣(a2﹣1),
=a2+4a+4﹣a2+1,
=4a+5
(40)原式=a8÷a2=a6;
(41)原式=a2b﹣6ab2+6ab2
=a2b.
(42)原式=a2b2﹣4ab+4ab=a2b2;
(43)原式=x2﹣xy﹣8xy+8y2=x2﹣9xy+8y2
(44)原式=27x6y3•(﹣5y)=﹣135x6y4;
(45)原式=(x2+y2+2xy﹣2xy﹣y2﹣4x)÷2x
=(x2﹣4x)÷2x
=
x﹣2
(46)原式=[(2x+a)+(2x﹣a)][(2x+a)﹣(2x﹣a)]
=(2x+a+2x﹣a)(2x+a﹣2x+a)
=4x•2a
=8ax;
(47)原式=(8x6﹣6x6﹣12x5)÷(﹣2x2)
=2(x6﹣6x5)÷(﹣2x2)
=﹣x4+6x3
=6x3﹣x4;
(48)原式=x2﹣4﹣(x2﹣2x﹣3)
=x2﹣4﹣x2+2x+3
=2x﹣1
(49)原式=8a3•b4÷12a3b2,
=
b2.
(50)原式=(6x2+9x﹣2x﹣3)﹣6x2
=6x2+9x﹣2x﹣3﹣6x2
=7x﹣3
(51)(﹣6x2)2+(﹣3x2)•x﹣27x5÷(﹣9x2)
=36x4﹣3x3+3x3=36x4
(52)(﹣2y2)3+y•y5
=﹣8y6+y6
=﹣7y6;
(53)(x+2)2﹣(x+1)(x﹣1)
=x2+4x+4﹣x2+1
=4x+5.
(54)原式=a2﹣b2+a2+2ab+b2﹣2a2﹣ab=ab.
(55)(﹣a)2•(a2)2÷a3
=a2•a4÷a3
=a6÷a3
=a3;
(56)(15x2y﹣10xy2)÷5xy=3x﹣2y
(57)原式=[8x6﹣6x6﹣12x5﹣6x4]÷x4
=[2x6﹣12x5﹣6x4]÷x4
=2x2﹣12x﹣6
(58)原式=(x+1)2+2(1﹣x)﹣x2=x2+2x+1+2﹣2x﹣x2=3.
(59)(12a3﹣6a2+3a)÷3a=4a2﹣2a+1;
(60)5x2(x+1)(x﹣1)=5x2(x2﹣1)
=5x4﹣5x2.
(61)原式=b2﹣4ab+4a2﹣4a2+4ab=b2
(62)原式=(﹣27a3b6)(﹣4ab2)
=108a4b8
(63)原式=3a2﹣18a﹣2a+12
=3a2﹣20a+12
(64)化成单项式除以单项式
﹣a+3b+7b2
(65)原式=x2﹣2x+3x﹣6﹣(x2﹣4x+4)=x2+x﹣6﹣x2+4x﹣4=5x﹣10;
(66)原式=9x2﹣16y2;
(67)原式=2x2﹣xy+6xy﹣3y2﹣5xy﹣3y2=2x2﹣6y2.
(68)原式=3a10•a6﹣4a6•a10=3a16﹣4a16=﹣a16;
(69)原式=4xy+x2﹣4xy+4y4+9y2﹣x2=4y4+9y2.
(70)原式=﹣3x2y2•4x2y2=﹣12x4y4;
(71)原式=a2﹣4ab+4b2+a2﹣4b2=2a2﹣4ab
(72)原式=a2﹣4b2﹣2ab+4b2
=a2﹣2ab
(73)原式=10x3﹣2x3=8x3
(74)原式=﹣8x3y6+6x3y6
=﹣2x3y6.
(75)原式=8x3×(﹣3xy2)=﹣24x4y2;
(76)原式=a2﹣2ab+3ab﹣6b2﹣(4a2﹣4ab+b2)
=a2﹣2ab+3ab﹣6b2﹣4a2+4ab﹣b2
=﹣3a2+5ab﹣7b2
(77)原式=﹣8x6y3+9x4•(﹣x2)•y3
=﹣8x6y3﹣9x6y3
=﹣17x6y3
(78)原式=﹣m10n4÷m2n2=﹣m8n2;
(79)原式=[(2a﹣1)(2a+1)]2=16a4﹣8a2+1;
(80)原式=
x2+2xy﹣
y2;
(81)原式=[2x﹣(3y﹣1)][2x+(3y﹣1)]=4x2﹣9y2+6y﹣1
(82)(﹣2x)(4x2﹣2x+1),
=﹣8x3+4x2﹣2x;
(83)(6a3﹣4a2+2a)÷2a,
=3a2﹣2a+1.
(84)(2x﹣y)(2x+y)﹣(x﹣3y)2,
=4x2﹣y2﹣x2+6xy﹣9y2,
=3x2+6xy﹣10y2.
(85)原式=﹣2x+x2﹣3﹣(2x﹣1)2
=﹣2x+x2﹣3﹣(4x2﹣4x+1)
=﹣2x+x2﹣3﹣4x2+4x﹣1
=x2﹣4x2﹣2x+4x﹣3﹣1
=﹣3x2+2x﹣4
(86)原式=(9m2+6mn+n2﹣6mn﹣n2)÷2m
=9m2÷2m
=
m
(87)原式=(x2y2+2x2y﹣x2y2+6x2y3)÷2x2y=(2x2y+6x2y3)÷2x2y=1+3y2
(88)原式=x6÷x2﹣
x2•27x2=x4﹣3x4=﹣2x4.
(89)原式=(2x+y)(2x﹣3y+4y)=(2x+y)(2x+y)=(2x+y)2
(90)原式=m2﹣4+m2+5m﹣m﹣5
=2m2+4m﹣9;
(91)原式=[x2+2xy+y2﹣(2xy+y2)﹣8x]÷2x
=(x2+2xy+y2﹣2xy﹣y2﹣8x)÷2x
=(x2﹣8x)÷2x
=
x﹣4.
(92).原式=2xy2÷2x﹣6xy÷2x+y2+2y=y2﹣3y+y2+2y=2y2﹣y
(93)原式=9a2﹣5a+2;
(94)原式=x2+2xy﹣x2﹣2x﹣1+2x
=2xy﹣1;
(95)原式=
x4y6÷(
x3y4)•(﹣4xy)
=
x4y6×
×(﹣4xy)
=
×(﹣4xy)
=﹣
;
(96)原式=a3+3+4a6+a6=a6+4a6+a6=6a6
(97)(2x+1)(x+3)﹣6(x2+x﹣1)
=2x2+6x+x+3﹣6x2﹣6x+6
=﹣4x2+x+9;
(98)[x(x2y2﹣xy)﹣y(x2﹣x3y)]+3x2y
=[x3y2﹣x2y﹣x2y+x3y2]+3x2y
=2x3y2﹣2x2y+3x2y
=2x3y2+x2y
(99)原式=[(2x+y)(2x+y﹣y)﹣4x]÷2x
=[(2x+y)×2x﹣4x]÷2x
=2x(2x+y﹣2)÷2x
=2x+y﹣2.
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