初一因式分解
\u521d\u4e00\u56e0\u5f0f\u5206\u89e3\u7ec3\u4e60\u9898\u53ca\u7b54\u6848\u4f60\u53ef\u771f\u72e0 \u8981\u8fd9\u4e48\u591a\u9898\u76ee
1. 5ax+5bx+3ay+3by
\u89e3\u6cd5\uff1a=5x(a+b)+3y(a+b)
=(5x+3y)(a+b)
2. x^3-x^2+x-1
\u89e3\u6cd5\uff1a=(x^3-x^2)+(x-1)
=x^2(x-1)+ (x-1)
=(x-1)(x^2+1)
3. x2-x-y2-y
\u89e3\u6cd5\uff1a=(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)\uff0e
x^2+3x-40
=x^2+3x+2.25-42.25
=(x+1.5)^2-(6.5)^2
=(x+8)(x-5)\uff0e
(x^2+x+1)(x^2+x+2)-12\u65f6\uff0c\u53ef\u4ee5\u4ee4y=x^2+x,\u5219
\u539f\u5f0f=(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)\uff0e
(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
\u89e3\uff1a\u539f\u5f0f=(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]\u00b7[(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
\u89e3\uff1a\u539f\u5f0f=(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)
\u5206\u89e3\u56e0\u5f0fm +5n-mn-5m
\u89e3\uff1am +5n-mn-5m= m -5m -mn+5n
= (m -5m )+(-mn+5n)
=m(m-5)-n(m-5)
=(m-5)(m-n)
\u5206\u89e3\u56e0\u5f0fbc(b+c)+ca(c-a)-ab(a+b)
\u89e3\uff1abc(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
\u7b54\u6848\uff1a1.(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\uff1d5p(3+2p)
\uff0d3x^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)
\u56e0\u5f0f\u5206\u89e33a3b2c\uff0d6a2b2c2\uff0b9ab2c3\uff1d3ab^2 c(a^2-2ac+3c^2)
3.\u56e0\u5f0f\u5206\u89e3xy\uff0b6\uff0d2x\uff0d3y\uff1d(x-3)(y-2)
4.\u56e0\u5f0f\u5206\u89e3x2(x\uff0dy)\uff0by2(y\uff0dx)\uff1d(x+y)(x-y)^2
5.\u56e0\u5f0f\u5206\u89e32x2\uff0d(a\uff0d2b)x\uff0dab\uff1d(2x-a)(x+b)
6.\u56e0\u5f0f\u5206\u89e3a4\uff0d9a2b2\uff1da^2(a+3b)(a-3b)
7.\u82e5\u5df2\u77e5x3\uff0b3x2\uff0d4\u542b\u6709x\uff0d1\u7684\u56e0\u5f0f\uff0c\u8bd5\u5206\u89e3x3\uff0b3x2\uff0d4\uff1d(x-1)(x+2)^2
8.\u56e0\u5f0f\u5206\u89e3ab(x2\uff0dy2)\uff0bxy(a2\uff0db2)\uff1d(ay+bx)(ax-by)
9.\u56e0\u5f0f\u5206\u89e3(x\uff0by)(a\uff0db\uff0dc)\uff0b(x\uff0dy)(b\uff0bc\uff0da)\uff1d2y(a-b-c)
10.\u56e0\u5f0f\u5206\u89e3a2\uff0da\uff0db2\uff0db\uff1d(a+b)(a-b-1)
11.\u56e0\u5f0f\u5206\u89e3(3a\uff0db)2\uff0d4(3a\uff0db)(a\uff0b3b)\uff0b4(a\uff0b3b)2\uff1d[3a-b-2(a+3b)]^2=(a-7b)^2
12.\u56e0\u5f0f\u5206\u89e3(a\uff0b3)2\uff0d6(a\uff0b3)\uff1d(a+3)(a-3)
13.\u56e0\u5f0f\u5206\u89e3(x\uff0b1)2(x\uff0b2)\uff0d(x\uff0b1)(x\uff0b2)2\uff1d-(x+1)(x+2) abc\uff0bab\uff0d4a\uff1da(bc+b-4)
(2)16x2\uff0d81\uff1d(4x+9)(4x-9)
(3)9x2\uff0d30x\uff0b25\uff1d(3x-5)^2
(4)x2\uff0d7x\uff0d30\uff1d(x-10)(x+3)
35.\u56e0\u5f0f\u5206\u89e3x2\uff0d25\uff1d(x+5)(x-5)
36.\u56e0\u5f0f\u5206\u89e3x2\uff0d20x\uff0b100\uff1d(x-10)^2
37.\u56e0\u5f0f\u5206\u89e3x2\uff0b4x\uff0b3\uff1d(x+1)(x+3)
38.\u56e0\u5f0f\u5206\u89e34x2\uff0d12x\uff0b5\uff1d(2x-1)(2x-5)
39.\u56e0\u5f0f\u5206\u89e3\u4e0b\u5217\u5404\u5f0f\uff1a (1)3ax2\uff0d6ax\uff1d3ax(x-2) (2)x(x\uff0b2)\uff0dx\uff1dx(x+1) (3)x2\uff0d4x\uff0dax\uff0b4a\uff1d(x-4)(x-a) (4)25x2\uff0d49\uff1d(5x-9)(5x+9) (5)36x2\uff0d60x\uff0b25\uff1d(6x-5)^2 (6)4x2\uff0b12x\uff0b9\uff1d(2x+3)^2 (7)x2\uff0d9x\uff0b18\uff1d(x-3)(x-6) (8)2x2\uff0d5x\uff0d3\uff1d(x-3)(2x+1) (9)12x2\uff0d50x\uff0b8\uff1d2(6x-1)(x-4)
40.\u56e0\u5f0f\u5206\u89e3(x\uff0b2)(x\uff0d3)\uff0b(x\uff0b2)(x\uff0b4)\uff1d(x+2)(2x-1)
41.\u56e0\u5f0f\u5206\u89e32ax2\uff0d3x\uff0b2ax\uff0d3\uff1d (x+1)(2ax-3)
42.\u56e0\u5f0f\u5206\u89e39x2\uff0d66x\uff0b121\uff1d(3x-11)^2
43.\u56e0\u5f0f\u5206\u89e38\uff0d2x2\uff1d2(2+x)(2-x)
44.\u56e0\u5f0f\u5206\u89e3x2\uff0dx\uff0b14 \uff1d\u6574\u6570\u5185\u65e0\u6cd5\u5206\u89e3
45.\u56e0\u5f0f\u5206\u89e39x2\uff0d30x\uff0b25\uff1d(3x-5)^2
46.\u56e0\u5f0f\u5206\u89e3\uff0d20x2\uff0b9x\uff0b20\uff1d(-4x+5)(5x+4)
47.\u56e0\u5f0f\u5206\u89e312x2\uff0d29x\uff0b15\uff1d(4x-3)(3x-5)
48.\u56e0\u5f0f\u5206\u89e336x2\uff0b39x\uff0b9\uff1d3(3x+1)(4x+3)
49.\u56e0\u5f0f\u5206\u89e321x2\uff0d31x\uff0d22\uff1d(21x+11)(x-2)
50.\u56e0\u5f0f\u5206\u89e39x4\uff0d35x2\uff0d4\uff1d(9x^2+1)(x+2)(x-2)
51.\u56e0\u5f0f\u5206\u89e3(2x\uff0b1)(x\uff0b1)\uff0b(2x\uff0b1)(x\uff0d3)\uff1d2(x-1)(2x+1)
52.\u56e0\u5f0f\u5206\u89e32ax2\uff0d3x\uff0b2ax\uff0d3\uff1d(x+1)(2ax-3)
53.\u56e0\u5f0f\u5206\u89e3x(y\uff0b2)\uff0dx\uff0dy\uff0d1\uff1d(x-1)(y+1)
54.\u56e0\u5f0f\u5206\u89e3(x2\uff0d3x)\uff0b(x\uff0d3)2\uff1d(x-3)(2x-3)
55.\u56e0\u5f0f\u5206\u89e39x2\uff0d66x\uff0b121\uff1d(3x-11)^2
56.\u56e0\u5f0f\u5206\u89e38\uff0d2x2\uff1d2(2-x)(2+x)
57.\u56e0\u5f0f\u5206\u89e3x4\uff0d1\uff1d(x-1)(x+1)(x^2+1)
58.\u56e0\u5f0f\u5206\u89e3x2\uff0b4x\uff0dxy\uff0d2y\uff0b4\uff1d(x+2)(x-y+2)
59.\u56e0\u5f0f\u5206\u89e34x2\uff0d12x\uff0b5\uff1d(2x-1)(2x-5)
60.\u56e0\u5f0f\u5206\u89e321x2\uff0d31x\uff0d22\uff1d(21x+11)(x-2)
61.\u56e0\u5f0f\u5206\u89e34x2\uff0b4xy\uff0by2\uff0d4x\uff0d2y\uff0d3\uff1d(2x+y-3)(2x+y+1)
62.\u56e0\u5f0f\u5206\u89e39x5\uff0d35x3\uff0d4x\uff1dx(9x^2+1)(x+2)(x-2)
x⁴-x²
=x²(x²-1)
=x²(x+1)(x-1)
a\uff08x²-y²\uff09+b\uff08y²-x²\uff09
=a(x²-y²)-b(x²-y²)
=(x²-y²)(a-b)
=(x+y)(x-y)(a-b)
-27x⁴+18x³-3x²
=-3x²(9x²-6x+1)
=-3x²(3x-1)²
x⁴-1
=(x²+1)(x²-1)
=(x²+1)(x+1)(x-1)
a⁴-2a²b²+b⁴
=(a²-b²)²
=(a+b)²(a-b)²
\uff08a²-a)²-\uff08a-1\uff09²
=[(a²-a)+(a-1)][(a²-a)-(a-1)]
=(a²-a+a-1)(a²-a-a+1)
=(a²-1)(a²+1)
=(a+1)(a-1)(a²+1)
=(-3)*(-3)^102+(-3)^102
=(-3+1)*(-3)^102
=-2*(-3)^102
2.1998^2-1999*1997
=1998^2-(1998-1)(1998+1)
=1998^2-1998^2+1
=1
3.(2^n+4)-2*(2^n)
--------------(此为分数线也就等于(2^n+4)-2*(2^n)/2*(2^n+3)）
2*(2^n+3)
=[2^(n+4)-2^(n+1)]/2^(n+4)
=[2^3*2^(n+1)-2^(n+1)]/[2^3*2^(n+1)]
=(2^3-1)/(2^3)
=7/8
4.利用因式分解说明(81^7)-(27^9)-(9^13)能被45整除
81^7-27^9-9^13
=(3^4)^7-(3^3)^9-(3^2)^13
=3^28-3^27-3^26
=3^24(3^4-3^3-2^2)
=3^24*(81-27-9)
=45*3^24
所以能被45整除
5.(a^2)+a+1=0,
（a^1980）+（a^1981）+（a^1982）+……+（a^2007）+（a^2008）+(a^2009)
=a^1980(1+a+a^2)+a^1983+……+a^2007+a^2008+a^2009
=a^1983+……+a^2007+a^2008+a^2009
=a^1983(1+a+a^2)+a^1986+……+a^2007+a^2008+a^2009
=a^1986+……+a^2007+a^2008+a^2009
如此反复提取公因式
=a^2007+a^2008+a^2009
=a^2007(1+a+a^2)
=0
6.（25^7）+（5^13）
=(5^2)^7+5^13
=5^14+5^13
=5^12(5^2+5)
=30*5^12
所以能被30整除
7.3a^2(2a+b)^2-27a^2b^2
=2a^2[(2a+b)^2-9b^2]
=2a^2(2a+b+3b)(2a+b-3b)
=8a^2(a+2b)(a-b)
8.4(x^2n)+20(x^n)(y^n)+25(y^2n)
完全平方
=(2x^n+5y^n)^2
9.{[(x^2)+1]^2}-4x[(x^2)+1]+4(x^2)
也是完全平方
=[(x^2+1)-2x]^2
=(x^2-2x+1)^2
=(x-1)^4
10.2(a^n)-(a^n+1)-(a^n+1)
=-a^(n-1)(a^2-2a+1)
=-a^(n-1)(a-1)^2
1.=-3*(-3)^102+(-3)^102=-2*(-3)^102=12^102
2.=1998^2-(1998+1)*(1998-1)=1998^2-1998^2+1^2=1
我先挂着，其他的等级分钟！！
1.（-3）的103次方+（-3）的102次方=（-3）的102次方*(-2)
利用因式分解化简
2.1998^2-1999*1997=1
3.(2^n+4)-2*(2^n)
--------------(此为分数线也就等于(2^n+4)-2*(2^n)/2*(2^n+3)）
2*(2^n+3)
4.利用因式分解说明(81^7)-(27^9)-(9^13)能被45整除 =3^26*5=3^24*45
5.利用饮食分解求值：若(a^2)+a+1=0,求（a^1980）+（a^1981）+（a^1982）+……+（a^2007）+（a^2008）+(a^2009)=a^1980*30个0=0的值
6.利用因式分解说明（25^7）+（5^13）=5^12*30能被30整除
7.3(a^2)[(2a+b)^2]-27(a^2)(b^2)
8.4(x^2n)+20(x^n)(y^n)+25(y^2n)
9.{[(x^2)+1]^2}-4x[(x^2)+1]+4(x^2)
10.2(a^n)-(a^n+1)-(a^n+1)(n是大于1的正数）
第一个，-（x-2y）的平方-z的平方。
第一题：添个负号，里面变一个就是完全平方式了。结果z^-（x-2y）^
1.(x-2y+z)(-x+2y+z)
=-(x-2y+z)(x-2y-z)
=-[(x-2y)^2-z^2](平方差）
=-x^2+4xy-4y^2+z^2
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绛旓細鍒濅竴鏁板 鍥犲紡鍒嗚В 寰堢畝鍗暵仿仿蜂贡绠鍗曠殑路路路鍙儨鎴戜笉浼 =m^2-n^2+2(m-n) =(m+n)(m-n)+2(m-n) =(m-n)(m+n+2)涓閬撻鐩,寰堢畝鍗,浣嗘垜涓嶄細鍋 659.4鍗冨厠 锛屽厔寮熺粰鍒嗗摝 鍛ㄩ暱C锛2蟺R灏辨槸鍗婂緞鍜屽渾鍛ㄧ巼鐨勭Н鐨2鍊 鍦嗛敟鐨勪綋绉疺=1/3鈭廟²h銆傚洜寮忓垎瑙 寰堢畝鍗 4...
绛旓細鈶㈢珛鏂瑰拰鍏紡锛歛3+b3=锛坅+b锛夛紙a2锛峚b+b2锛夌珛鏂瑰樊鍏紡锛歛3锛峛3=锛坅锛峛锛夛紙a2+ab+b2锛夛紙3锛夊垎缁勫垎瑙ｆ硶鈥斺斿埄鐢ㄥ垎缁勬潵鍒嗚В鍥犲紡鐨勬柟娉曞彨鍋氬垎缁勫垎瑙ｆ硶锛庤鍒嗚В鐨勫椤瑰紡涓紝濡傛灉椤规暟瓒呰繃涓夐」锛岃繘琛鍥犲紡鍒嗚В鏃舵墍閲囩敤鐨勬柟娉曞父鏄垎缁勫垎瑙ｏ紟涓鑸潵璇达紝鍒嗙粍鍒嗚В娉曟湁涓ょ绫诲瀷锛氱涓绉嶆槸鍒嗙粍鍚庡悇缁勬湁鍏洜寮...
绛旓細1銆佹彁鍙栧叕鍥犲紡娉曪紝鎶婂悇椤逛腑鐨勫叕鍥犲紡鎴栧叕鍥犳暟鎻愬彇锛岀壒鍒笉璁╀汉娉ㄦ剰鐨勫洜鏁板線寰琚 浜哄拷鐣ワ紱2銆佸畬鍏ㄥ钩鏂瑰叕寮忥細椤规暟鈥斺斾笁椤癸紝婊¤冻瀹屽叏骞虫柟鍏紡鈥斺(a卤b)^2=a^2卤2ab+b^2銆3銆佸钩鏂瑰樊鍏紡锛氶」鏁扳斺斾袱椤癸紝婊¤冻涓ゅ紡骞虫柟鍏紡鐨勫舰寮忊斺攁^2-b^2=(a+b)(a-b).4銆佷换浣曚竴涓洜寮忓垎瑙ｉ鍏堢湅鏄惁鏈...
绛旓細锛1锛6*x鐨勫钩鏂+5xy-6*y鐨勫钩鏂-6xz+4yz =(3x-2y)*(2x+3y)-2z*(3x-2y)=(3x-2y)*(2x+3y-2z)锛2锛墄鐨勫钩鏂-xy+2x+y-3 =(x^2+3x-4)-(xy+x)+(y+1)=(x-1)(x+4)-x(y+1)+(y+1)=(x-1)(x+4)-(y+1)(x-1)=(x-1)(x-y+3)...
绛旓細鍒濅竴鍖栫畝棰樺彲浠ョ敤鍥犲紡鍒嗚В娉曘佹彁鍏洜寮忔硶銆佸叕寮忔硶銆佸垎缁勬硶鏉ュ仛銆備竴銆佸洜寮忓垎瑙ｆ硶 鍥犲紡鍒嗚В娉曟槸涓绉嶅父瑙佺殑鏁板鏂规硶锛岄氳繃灏嗕竴涓椤瑰紡鍒嗚В涓鸿嫢骞蹭釜鍥犲紡锛屼娇寰楁瘡涓洜寮忛兘鍙互鏇村鏄撳湴瑙ｅ喅銆傚湪鍒濅竴鏁板涓紝鍥犲紡鍒嗚В娉曢氬父鐢ㄤ簬绠鍖栧鏉傜殑澶氶」寮忥紝鎻愬彇鍏洜寮忓拰瑙ｅ喅涓鍏冧簩娆℃柟绋嬬瓑闂銆傛帉鎻″洜寮忓垎瑙ｆ硶瀵逛簬鎻愰珮鏁板...
绛旓細=(x^2-4xy+4y^2)/4(x-2y)=(x-2y)(x-2y)/4(x-2y)=(x-2y)/4 (x-1)^2=(x-1)(x+1)瑙ｏ細(x-1)^2-(x-1)(x+1)=0 (x-1)[(x-1)-(x+1)]=0 (x-1)脳(-2)=0 x-1=0 x=1 9^13-3^24 =9^13-9^12 =9脳9^12-9^12 =8脳9^12 鎵浠9^13-3^24鑳借8...
绛旓細1銆佸崟椤瑰紡12ab³涓-18a³b²鐨勫叕鍥犲紡鏄6ab²(2b²-3a²)2銆鍥犲紡鍒嗚В:36-x²=(6-x)(6+x).3銆佸洜寮忓垎瑙:4y²-4y+1=(2y-1)².4銆佸洜寮忓垎瑙:a(b-c)+b(b-c)=(a+b)(b-c).5銆佸洜寮忓垎瑙:4鍒嗕箣1x²-25y²=(1/2x+5y...
绛旓細骞虫柟宸叕寮忥細a^2-b^2=(a+b)(a-b)x^2-(x-y)^2=[x+锛坸-y锛塢[x-锛坸-y)]=(2x-y)*y=2xy-y^2 4x^2-(x-y)^2=(2x)^2-(x-y)^2=[2x+锛坸-y锛塢[2x-锛坸-y)]=(3x-y)(x+y)=3x^2+2xy-y^2 -(a+b)^2+(2a-3b)^2=(2a-3b)^2-(a+b)^2=[(2a-3b)+(a...
