Question

初中数学因式分解题

（1）xy-xz-y²+2yz-z²
（2）2x²+xy-y²-4x+5y-6

Answer 1

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)
要给分啊

Answer 2

原式=x(y-z)-(y²-2yz+z²)
=x(y-z)-(y-z)²
=(y-z)(x-y+z)

原式=(x+y)(2x-y)-4x+5y-6
x+y -3
×
2x-y 2
所以原式=(x+y-3)(2x-y+2)

Answer 3

（1）xy-xz-y²+2yz-z²
=x(y-z)-(y-z)²
=(y-z)(x-y+z)
（2）2x²+xy-y²-4x+5y-6
=(x+y)(2x-y)-4x+5y-6
=(x+y-3)(2x-y+2)

Answer 4

1)x(y-z)-(y-z)^2=(y-z)(x-(y-z))=(y-z)(x-y+z)
2)想了半天，也没能做不来