初一因式分解练习题及答案

你可真狠 要这么多题目

1. 5ax+5bx+3ay+3by
解法：=5x(a+b)+3y(a+b)
=(5x+3y)(a+b)
2. x^3-x^2+x-1
解法：=(x^3-x^2)+(x-1)
=x^2(x-1)+ (x-1)
=(x-1)(x^2+1)
3. x2-x-y2-y
解法：=(x2-y2)-(x+y)
=(x+y)(x-y)-(x+y)
=(x+y)(x-y-1)

bc(b+c)+ca(c-a)-ab(a+b)
=bc(c-a+a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+bc(a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)
=(bc+ca)(c-a)+(bc-ab)(a+b)
=c(c-a)(b+a)+b(a+b)(c-a)
=(c+b)(c-a)(a+b)．

x^2+3x-40
=x^2+3x+2.25-42.25
=(x+1.5)^2-(6.5)^2
=(x+8)(x-5)．

(x^2+x+1)(x^2+x+2)-12时，可以令y=x^2+x,则
原式=(y+1)(y+2)-12
=y^2+3y+2-12=y^2+3y-10
=(y+5)(y-2)
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)．

(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2

解：原式=(1+y)^2+2(1+y)x^2(1+y)+x^4(1-y)^2-2(1+y)x^2(1-y)-2x^2(1+y^2)

=[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2)

=[(1+y)+x^2(1-y)]^2-(2x)^2

=[(1+y)+x^2(1-y)+2x]·[(1+y)+x^2(1-y)-2x]

=(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1)

=[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)]

=(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)

x^5+3x^4y-5x^3y^2+4xy^4+12y^5

解：原式=(x^5+3x^4y)-(5x^3y^2+15x^2y^3)+(4xy^4+12y^5)

=x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y)

=(x+3y)(x^4-5x^2y^2+4y^4)

=(x+3y)(x^2-4y^2)(x^2-y^2)

=(x+3y)(x+y)(x-y)(x+2y)(x-2y)

分解因式m +5n-mn-5m
解：m +5n-mn-5m= m -5m -mn+5n
= (m -5m )+(-mn+5n)
=m(m-5)-n(m-5)
=(m-5)(m-n)

分解因式bc(b+c)+ca(c-a)-ab(a+b)
解：bc(b+c)+ca(c-a)-ab(a+b)=bc(c-a+a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)
=c(c-a)(b+a)+b(a+b)(c-a)
=(c+b)(c-a)(a+b)

1.(2a-b)²+8ab
2.y²-2y-x²+1
3.x²-xy+yz-xz
4.6x²+5x-4
5.2a²-7ab+6b²
6.(x²-2x)²+2(x²-2x)+1
7.(x²-2x)²-14(x²-2x)-15
8.x²(x-y)+(y-x)
9.169(a+b)²-121(a-b)²
10.(x-3)(x-5)+1
答案：1.(2a-b)²+8ab=(2a+b)²
2.y²-2y-x²+1=(y-1)²-x²=(y-1-x)(y-1+x)
3.x²-xy+yz-xz =x(x-y)-z(x-y)=(x-z)(x-y)
4.6x²+5x-4 =(2x-1)(3x+4)
5.2a²-7ab+6b²=(2a-3b)(a-2b)
6.(x²-2x)²+2(x²-2x)+1 =(x²-2x+1)²=(x-1)^4
7.(x²-2x)²-14(x²-2x)-15 =(x²-2x-15)(x²-2x+1)=(x+3)(x-5)(x-1)²
8.x²(x-y)+(y-x) =(x²-1)(x-y)=(x+1)(x-1)(x-y)
9.169(a+b)²-121(a-b)²
=(14a+14b-11a+11b)(14a+14b+11a-11b)
=(3a+25b)(25a+3b)
10.(x-3)(x-5)+1 =(x-3)²-2(x-3)+1 =(x-3-1)²=(x-4)²

-5a^2+16a=a(16-5a)
8x^2-4x=4x(2x-1)
15p+10p^2＝5p(3+2p)
－3x^2y-6xy=-3xy(x+2y)
14m^3n^2-6m^2n^3=2m^2n^2(7m-6n)
27a^2 b^3 c+18ab^2=9ab^2(3abc+2)
18xy^2 z^3+12x^2 y^2=6xy^2(3z^3+2x)
8m^2 n^2 -6m^3 n^2=2m^2 n^2(4-3m)

因式分解3a3b2c－6a2b2c2＋9ab2c3＝3ab^2 c(a^2-2ac+3c^2)
3.因式分解xy＋6－2x－3y＝(x-3)(y-2)
4.因式分解x2(x－y)＋y2(y－x)＝(x+y)(x-y)^2
5.因式分解2x2－(a－2b)x－ab＝(2x-a)(x+b)
6.因式分解a4－9a2b2＝a^2(a+3b)(a-3b)
7.若已知x3＋3x2－4含有x－1的因式，试分解x3＋3x2－4＝(x-1)(x+2)^2
8.因式分解ab(x2－y2)＋xy(a2－b2)＝(ay+bx)(ax-by)
9.因式分解(x＋y)(a－b－c)＋(x－y)(b＋c－a)＝2y(a-b-c)
10.因式分解a2－a－b2－b＝(a+b)(a-b-1)
11.因式分解(3a－b)2－4(3a－b)(a＋3b)＋4(a＋3b)2＝[3a-b-2(a+3b)]^2=(a-7b)^2
12.因式分解(a＋3)2－6(a＋3)＝(a+3)(a-3)
13.因式分解(x＋1)2(x＋2)－(x＋1)(x＋2)2＝-(x+1)(x+2) abc＋ab－4a＝a(bc+b-4)
(2)16x2－81＝(4x+9)(4x-9)
(3)9x2－30x＋25＝(3x-5)^2
(4)x2－7x－30＝(x-10)(x+3)
35.因式分解x2－25＝(x+5)(x-5)
36.因式分解x2－20x＋100＝(x-10)^2
37.因式分解x2＋4x＋3＝(x+1)(x+3)
38.因式分解4x2－12x＋5＝(2x-1)(2x-5)
39.因式分解下列各式： (1)3ax2－6ax＝3ax(x-2) (2)x(x＋2)－x＝x(x+1) (3)x2－4x－ax＋4a＝(x-4)(x-a) (4)25x2－49＝(5x-9)(5x+9) (5)36x2－60x＋25＝(6x-5)^2 (6)4x2＋12x＋9＝(2x+3)^2 (7)x2－9x＋18＝(x-3)(x-6) (8)2x2－5x－3＝(x-3)(2x+1) (9)12x2－50x＋8＝2(6x-1)(x-4)
40.因式分解(x＋2)(x－3)＋(x＋2)(x＋4)＝(x+2)(2x-1)
41.因式分解2ax2－3x＋2ax－3＝ (x+1)(2ax-3)
42.因式分解9x2－66x＋121＝(3x-11)^2
43.因式分解8－2x2＝2(2+x)(2-x)
44.因式分解x2－x＋14 ＝整数内无法分解
45.因式分解9x2－30x＋25＝(3x-5)^2
46.因式分解－20x2＋9x＋20＝(-4x+5)(5x+4)
47.因式分解12x2－29x＋15＝(4x-3)(3x-5)
48.因式分解36x2＋39x＋9＝3(3x+1)(4x+3)
49.因式分解21x2－31x－22＝(21x+11)(x-2)
50.因式分解9x4－35x2－4＝(9x^2+1)(x+2)(x-2)
51.因式分解(2x＋1)(x＋1)＋(2x＋1)(x－3)＝2(x-1)(2x+1)
52.因式分解2ax2－3x＋2ax－3＝(x+1)(2ax-3)
53.因式分解x(y＋2)－x－y－1＝(x-1)(y+1)
54.因式分解(x2－3x)＋(x－3)2＝(x-3)(2x-3)
55.因式分解9x2－66x＋121＝(3x-11)^2
56.因式分解8－2x2＝2(2-x)(2+x)
57.因式分解x4－1＝(x-1)(x+1)(x^2+1)
58.因式分解x2＋4x－xy－2y＋4＝(x+2)(x-y+2)
59.因式分解4x2－12x＋5＝(2x-1)(2x-5)
60.因式分解21x2－31x－22＝(21x+11)(x-2)
61.因式分解4x2＋4xy＋y2－4x－2y－3＝(2x+y-3)(2x+y+1)
62.因式分解9x5－35x3－4x＝x(9x^2+1)(x+2)(x-2)

1）a的四次方+a²+1
=a^4+2a²+1-a²
=(a²+1)²-a²
=(a²+a+1)(a²-a+1)
（2）2a²-7ab+6b²
=(2a-3b)(a-2b)
（3）3x²+xy-2y²
=(3x-2y)(x+y)
（4）10a²b²+11ab-6
=(2ab+3)(5ab-2)
（5）7a³x-28a（x的五次方）
=7a³(x-4a²)
（6）x³-10x²+16x
=x(x²-10x+16)
=x(x-2)(x-8)
（7）（x²+3x）²-2（x²+3x）-8
=(x²+3x+2)(x²+3x-4)
=(x+1)(x+2)(x+4)(x-1)
（8）（x-y）²+4xy-1
=x²-2xy+y²+4xy-1
=x²+2xy+y²-1
=(x+y)²-1
=(x+y+1)(x+y-1)
9.x^2 -4xy +4y^2 -x +2y -2
= (x-2y)^2 - (x-2y) -2
=(x-2y + 1)(x-2y-2)
10.x³+ax²+bx²+cx²+abx+bcx+acx+ab
=x³+cx²+abx+abc+bx²+bcx+ax²+acx
=x²(x+c)+ab(x+c)+bx(x+c)+ax(x+c)
=(x+c)[x²+bx+ab+ax]
=(x+c)[x(x+b)+a(x+b)]
=(x+a)(x+b)(x+c)

11.x²-y²-y-1/2
=x²-(y²+y+1/4)
=x²-(y+1/2)²
=(x+y+1/2)(x-y-1/2)
12.x的四次方+3x³+6x ² -4
=x^4+x³+2x³+2x²+4(x²-1)
=x³(x+1)+2x²(x+1)+(4x-4)(x+1)
=(x+1)(x³+2x²+4x-4)
13.x³-3x²+4
=x³+1-3(x²-1)
=(x+1)(x²-x+1)-(3x-3)(x+1)
=(x+1)(x²-4x+4)
=(x+1)(x-2)²
14.32a[(x^2+2x)^2]-2a
=2a[16(x^2+2x)^2-1]
=2a(4x^2+8x+1)(4x^2+8x-1)

15.16+8(x^2+4x)+(x^2+4x)^2
=(4+x^2+4x)^2
=(x^2+4x+4)^2
=(x+2)^4

16.3x^ny+9x^(n-1)y^2+x^(n+1)/4
=x^(n-1)(3xy+9y^2+x^2/4)
=x^(n-1)(x^2/4+3xy+9y^2)
=x^(n-1)(x/2+3y)^2
=(1/4)[x^(n-1)](x+6y)^2
17.a^4+a³+3a-5
=a²*(a²+a)+3a-5
=3a²+3a-5
=3(a²+a)-5
18.1+x+x(x+1)+x(x+1)^2+x(x+1)^3
=(1+x)+x(x+1)+x(x+1)^2+x(x+1)^3
=(1+x)(1+x)+x(x+1)^2+x(x+1)^3
=(1+x)²(1+x)+x(x+1)^3
=(1+x)³(1+x)
=(1+x)^4
19. (x-y)(2x-2y-3)-2
=(x-y)[2(x-y)-3]-2
=2(x-y) ^2-3(x-y)-2
=[(x-y)-2][2(x-y)+1]
=(x-y-2)(2x-2y+1).
x2-3xy-10y2+x+9y-2=(x-5y+2)(x+2y-1)．
x2-y2+5x+3y+4=(x+y+1)(x-y+4)．
xy+y2+x-y-2=(y+1)(x+y-2)．
6x2-7xy-3y2-xz+7yz-2z2=(2x-3y+z)(3x+y-2z)．
a^2+2b^2+3c^2+3aB+4ac+5bc =(a+b+c)(a+2b+3c)
x^2-8x+7 =（x-1）（x-7）
X^2+8X+7= (x+1)(x+7)
X^2-10X-11 =(x-11)(x+1)
x^2+10X-11= ，(x+11)(x-1)
X^+3x-18 =(x+6)(x-3)
x^2+11X+18 =(x+2)(x+9)
x^2-11x+18 =(x-2)(x-9)
x^2+17X-18 =(x+18)(x-1)
X^2-17X-18 =( x-18)(x+1)
xy＋6－2x－3y＝(x-3)(y-2)
x2(x－y)＋y2(y－x)＝(x+y)(x-y)^2
2x2－(a－2b)x－ab＝(2x-a)(x+b)
a4－9a2b2＝a^2(a+3b)(a-3b)
x3＋3x2－4＝(x-1)(x+2)^2
ab(x2－y2)＋xy(a2－b2)＝(ay+bx)(ax-by)
(x＋y)(a－b－c)＋(x－y)(b＋c－a)＝2y(a-b-c)
a2－a－b2－b＝(a+b)(a-b-1)
(3a－b)2－4(3a－b)(a＋3b)＋4(a＋3b)2＝[3a-b-2(a+3b)]^2=(a-7b)^2
(x＋1)2(x＋2)－(x＋1)(x＋2)2＝-(x+1)(x+2)
abc＋ab－4a＝a(bc+b-4)
16x2－81＝(4x+9)(4x-9)
9x2－30x＋25＝(3x-5)^2
x2－7x－30＝(x-10)(x+3)
x2－25＝(x+5)(x-5)
x2＋4x＋3＝(x+1)(x+3)
4x2－12x＋5＝(2x-1)(2x-5)
3ax2－6ax＝3ax(x-2)
x(x＋2)－x＝x(x+1)
x2－4x－ax＋4a＝(x-4)(x-a)
25x2－49＝(5x-9)(5x+9)
36x2－60x＋25＝(6x-5)^2
4x2＋12x＋9＝(2x+3)^2
x2－9x＋18＝(x-3)(x-6)
2x2－5x－3＝(x-3)(2x+1)
12x2－50x＋8＝2(6x-1)(x-4)
(x＋2)(x－3)＋(x＋2)(x＋4)＝(x+2)(2x-1)
2ax2－3x＋2ax－3＝ (x+1)(2ax-3)
9x2－66x＋121＝(3x-11)^2
8－2x2＝2(2+x)(2-x)
9x2－30x＋25＝(3x-5)^2
－20x2＋9x＋20＝(-4x+5)(5x+4)
12x2－29x＋15＝(4x-3)(3x-5)
36x2＋39x＋9＝3(3x+1)(4x+3)
21x2－31x－22＝(21x+11)(x-2)
9x4－35x2－4＝(9x^2+1)(x+2)(x-2)
(2x＋1)(x＋1)＋(2x＋1)(x－3)＝2(x-1)(2x+1)
2ax2－3x＋2ax－3＝(x+1)(2ax-3)
x(y＋2)－x－y－1＝(x-1)(y+1)
(x2－3x)＋(x－3)2＝(x-3)(2x-3)
9x2－66x＋121＝(3x-11)^2
8－2x2＝2(2-x)(2+x)
x4－1＝(x-1)(x+1)(x^2+1)
x2＋4x－xy－2y＋4＝(x+2)(x-y+2)
4x2－12x＋5＝(2x-1)(2x-5)
21x2－31x－22＝(21x+11)(x-2)
4x2＋4xy＋y2－4x－2y－3＝(2x+y-3)(2x+y+1)
9x5－35x3－4x＝x(9x^2+1)(x+2)(x-2)
3x2－6x＝3x(x-2)
49x2－25＝(7x+5)(7x-5)
6x2－13x＋5＝(2x-1)(3x-5)
x2＋2－3x＝(x-1)(x-2)
12x2－23x－24＝(3x-8)(4x+3)
(x＋6)(x－6)－(x－6)＝(x-6)(x+5)
3(x＋2)(x－5)－(x＋2)(x－3)＝2(x-6)(x+2)
9x2＋42x＋49＝(3x+7)^2 。
3a3b2c－6a2b2c2＋9ab2c3＝3ab^2 c(a^2-2ac+3c^2)
xy＋6－2x－3y＝(x-3)(y-2)
x2(x－y)＋y2(y－x)＝(x+y)(x-y)^2
2x2－(a－2b)x－ab＝(2x-a)(x+b)
x^3+2x^2-16x-32=(x+2)(x+4)(x-4)
(a-b)a^6+（b-a)b^6=(a-b)^2(a^2+ab+b^2)(a+b)(a^2-ab+b^2)
(x+y)(x+y+2xy)+(xy+1)(xy-1) =(x+1)(y+1)(x+y+xy-1)
X^8+X^7+1 =（X^2+X+1）（X^6-X^4+X^3-X+1）
x^8+x^6+x^4+x^2+1 =(x^4+x^3-x+1)(x^4+x^3+x^2+x+1)

x^2－20x＋100＝(x-10)^2
x^2-3x+2=(x-1)(x-2)
x^2-2x-15=(x+3)(x-5)
x^2+2x-15=(x-3)(x+5)
x^2-7x+12=(x-3)(x-4)
x^2-7x-30=(x+3)(x-10)
x^2+2x-3=(x-1)(x+3)
x^2-16x+64=(x-8)^2
x^2-9x+20=(x-4)(x-5)
x^2-6x+8=(x-2)(x-4)
x^2-6x-7=(x-7)(x+1)