Question

30道因式分解练习题及过程

Answer 1

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 
   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 
   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 
   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) 
   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)

   请采纳谢谢

Answer 2

你没有图哦，采纳我吧