将真题分解并练习
解:=5x(a+b)+3y(a+b)
=(5x+3y)(a+b)
2.x^3-x^2+x-1
解:=(x ^ 3-x ^ 2)+(x-1)
=x^2(x-1)+ (x-1)
=(x-1)(x^2+1)
3.x2-x-y2-y
解:=(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，可以使y = x 2+x，那么
原公式=(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
原公式=(1+y)2+2(1+y)x2(1+y)+x4(1-y)2-2(1+y)x。
=[(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
原公式=(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)
分解因子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)
分解因子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)？+8ab
2.y？-2y-x？+1
3.x？-xy+yz-xz
4.6x？+5x-4
5.2a？-7ab+6b？
6.(x？-2x)？+2(x？-2x)+1
7.(x？-2x)？-14(x？-2x)-15
8.x？(x-y)+(y-x)
9.169(a+b)？-121(a-b)？
10.(x-3)(x-5)+1
答案:1。(2a-b)？+8ab=(2a+b)？
2.y？-2y-x？+1=(y-1)？-x？=(y-1-x)(y-1+x)
3.x？-xy+yz-xz = x(x-y)-z(x-y)=(x-z)(x-y)
4.6x？+5x-4 =(2x-1)(3x+4)
5.2a？-7ab+6b？=(2a-3b)(a-2b)
6.(x？-2x)？+2(x？-2x)+1 =(x？-2x+1)？=(x-1)^4
7.(x？-2x)？-14(x？-2x)-15 =(x？-2x-15)(x？-2x+1)=(x+3)(x-5)(x-1)？
8.x？(x-y)+(y-x) =(x？-1)(x-y)=(x+1)(x-1)(x-y)
9.169(a+b)？-121(a-b)？
=(14a+14 B- 11a+11b)(14a+14 b+11a-11b)
=(3a+25b)(25a+3b)
10.(x-3)(x-5)+1 =(x-3)？-2(x-3)+1 =(x-3-1)？=(x-4)？
-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-6a2b2c 2+9ab 2c 3 = 3ab 2c(a2-2ac+3c 2)
3.因子分解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.如果已知x3+3x2-4包含x-1的因子，试着分解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)2 =-(x+1)(x+2)ABC+A B- 4A = A(。
(2)16x 2-81 =(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.因子分解x2-20x+100 = (x-10) 2
37.因式分解x2+4x+3 = (x+1) (x+3)
38.因式分解4x 2-12x+5 =(2x-1)(2x-5)
39.分解以下几类:(1)3 ax2-6ax = 3ax(x-2)(2)x(x+2)-x = x(x+1)(3)x2-4x-ax+4a =(x-4)。4x2+12x+9=(2x+3)^2(7)x2-9x+18 =(x-3)(x-6)(8)2x 2-5x-3 =(x-3)(2x+1)(9)12x 2-50x+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2 ax2-3x+2ax-3 =(x+1)(2ax-3)
42.因式分解9 x2-66x+121 =(3x-11)2
43.因式分解8-2x2 = 2 (2+x) (2-x)
44.因式分解X2-X+14 =它不能在整数内分解。
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12 x2-29x+15 =(4x-3)(3x-5)
48.因式分解36x2+39x+9 = 3 (3x+1) (4x+3)。
49.因式分解21x 2-31x-22 =(21x+11)(x-2)
50.因式分解9 x4-35 x2-4 =(9 x2+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2 ax2-3x+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9 x2-66x+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4x 2-12x+5 =(2x-1)(2x-5)
60.因式分解21x 2-31x-22 =(21x+11)(x-2)
61.因式分解4x 2+4xy+y2-4x-2y-3 =(2x+y-3)(2x+y+1)
62.因式分解9x 5-35x 3-4x = X(9 x2+1)(X+2)(X-2)