15道因式分解，解题过程要完整，急求，谢谢！ 15道数学题，很急 因式分解
\u6c4215\u9053\u521d\u4e8c\u56e0\u5f0f\u5206\u89e3\u7684\u9898\u76ee \u4e0e\u8be6\u7ec6\u89e3\u9898\u8fc7\u7a0b\u2026\u2026\u8981\u6076\u8865\u4e00\u4e0b\u4e86 \u9ad8\u5206\u60ac\u8d4f(1)-6ax3y+8x2y2-2x2y
(2)3a2(x-y)3-4b2(y-x)2
(3)(x+y)(m-a)-3y(a-m)2+(a-m)3
(4)8x(a-1)-4(1-a)
(5)m(1-a)+mn(1-a)+1-a
(1)16x4-64y4
(2)16x6-1/4
(3)(a6+b4)2-4a6b4
(5)-2m8+512
(6)(x+y)3-64 \u6216m3-64n3
\u5206\u89e3\u56e0\u5f0f\uff1ax^3-4x^2+6x-4
\u56e0\u5f0f\u5206\u89e3\u7684\u5341\u4e8c\u79cd\u65b9\u6cd5 :
\u628a\u4e00\u4e2a\u591a\u9879\u5f0f\u5316\u6210\u51e0\u4e2a\u6574\u5f0f\u7684\u79ef\u7684\u5f62\u5f0f\uff0c\u8fd9\u79cd\u53d8\u5f62\u53eb\u505a\u628a\u8fd9\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u3002\u56e0\u5f0f\u5206\u89e3\u7684\u65b9\u6cd5\u591a\u79cd\u591a\u6837\uff0c\u73b0\u603b\u7ed3\u5982\u4e0b\uff1a
1\u3001 \u63d0\u516c\u56e0\u6cd5
\u5982\u679c\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u5404\u9879\u90fd\u542b\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u628a\u8fd9\u4e2a\u516c\u56e0\u5f0f\u63d0\u51fa\u6765\uff0c\u4ece\u800c\u5c06\u591a\u9879\u5f0f\u5316\u6210\u4e24\u4e2a\u56e0\u5f0f\u4e58\u79ef\u7684\u5f62\u5f0f\u3002
\u4f8b1\u3001 \u5206\u89e3\u56e0\u5f0fx -2x -x(2003\u6dee\u5b89\u5e02\u4e2d\u8003\u9898)
x -2x -x=x(x -2x-1)
2\u3001 \u5e94\u7528\u516c\u5f0f\u6cd5
\u7531\u4e8e\u5206\u89e3\u56e0\u5f0f\u4e0e\u6574\u5f0f\u4e58\u6cd5\u6709\u7740\u4e92\u9006\u7684\u5173\u7cfb\uff0c\u5982\u679c\u628a\u4e58\u6cd5\u516c\u5f0f\u53cd\u8fc7\u6765\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u7528\u6765\u628a\u67d0\u4e9b\u591a\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u3002
\u4f8b2\u3001\u5206\u89e3\u56e0\u5f0fa +4ab+4b (2003\u5357\u901a\u5e02\u4e2d\u8003\u9898)
\u89e3\uff1aa +4ab+4b =\uff08a+2b\uff09
3\u3001 \u5206\u7ec4\u5206\u89e3\u6cd5
\u8981\u628a\u591a\u9879\u5f0fam+an+bm+bn\u5206\u89e3\u56e0\u5f0f\uff0c\u53ef\u4ee5\u5148\u628a\u5b83\u524d\u4e24\u9879\u5206\u6210\u4e00\u7ec4\uff0c\u5e76\u63d0\u51fa\u516c\u56e0\u5f0fa\uff0c\u628a\u5b83\u540e\u4e24\u9879\u5206\u6210\u4e00\u7ec4\uff0c\u5e76\u63d0\u51fa\u516c\u56e0\u5f0fb\uff0c\u4ece\u800c\u5f97\u5230a(m+n)+b(m+n),\u53c8\u53ef\u4ee5\u63d0\u51fa\u516c\u56e0\u5f0fm+n\uff0c\u4ece\u800c\u5f97\u5230(a+b)(m+n)
\u4f8b3\u3001\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)
4\u3001 \u5341\u5b57\u76f8\u4e58\u6cd5
\u5bf9\u4e8emx +px+q\u5f62\u5f0f\u7684\u591a\u9879\u5f0f\uff0c\u5982\u679ca\u00d7b=m,c\u00d7d=q\u4e14ac+bd=p\uff0c\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3a(ax+d)(bx+c)
\u4f8b4\u3001\u5206\u89e3\u56e0\u5f0f7x -19x-6
\u5206\u6790\uff1a 1 -3
7 2
2-21=-19
\u89e3\uff1a7x -19x-6=\uff087x+2\uff09(x-3)
5\u3001\u914d\u65b9\u6cd5
\u5bf9\u4e8e\u90a3\u4e9b\u4e0d\u80fd\u5229\u7528\u516c\u5f0f\u6cd5\u7684\u591a\u9879\u5f0f\uff0c\u6709\u7684\u53ef\u4ee5\u5229\u7528\u5c06\u5176\u914d\u6210\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u7136\u540e\u518d\u5229\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\uff0c\u5c31\u80fd\u5c06\u5176\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b5\u3001\u5206\u89e3\u56e0\u5f0fx +3x-40
\u89e3x +3x-40=x +3x+( ) -( ) -40
=(x+ ) -( )
=(x+ + )(x+ - )
=(x+8)(x-5)
6\u3001\u62c6\u3001\u6dfb\u9879\u6cd5
\u53ef\u4ee5\u628a\u591a\u9879\u5f0f\u62c6\u6210\u82e5\u5e72\u90e8\u5206\uff0c\u518d\u7528\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b6\u3001\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)
7\u3001 \u6362\u5143\u6cd5
\u6709\u65f6\u5728\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u591a\u9879\u5f0f\u4e2d\u7684\u76f8\u540c\u7684\u90e8\u5206\u6362\u6210\u53e6\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u7136\u540e\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6700\u540e\u518d\u8f6c\u6362\u56de\u6765\u3002
\u4f8b7\u3001\u5206\u89e3\u56e0\u5f0f2x -x -6x -x+2
\u89e3\uff1a2x -x -6x -x+2=2(x +1)-x(x +1)-6x
=x [2(x + )-(x+ )-6
\u4ee4y=x+ , x [2(x + )-(x+ )-6
= x [2(y -2)-y-6]
= x (2y -y-10)
=x (y+2)(2y-5)
=x (x+ +2)(2x+ -5)
= (x +2x+1) (2x -5x+2)
=(x+1) (2x-1)(x-2)
8\u3001 \u6c42\u6839\u6cd5
\u4ee4\u591a\u9879\u5f0ff(x)=0,\u6c42\u51fa\u5176\u6839\u4e3ax ,x ,x ,\u2026\u2026x ,\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3af(x)=(x-x )(x-x )(x-x )\u2026\u2026(x-x )
\u4f8b8\u3001\u5206\u89e3\u56e0\u5f0f2x +7x -2x -13x+6
\u89e3\uff1a\u4ee4f(x)=2x +7x -2x -13x+6=0
\u901a\u8fc7\u7efc\u5408\u9664\u6cd5\u53ef\u77e5\uff0cf(x)=0\u6839\u4e3a \uff0c-3\uff0c-2\uff0c1
\u52192x +7x -2x -13x+6=(2x-1)(x+3)(x+2)(x-1)
9\u3001 \u56fe\u8c61\u6cd5
\u4ee4y=f(x)\uff0c\u505a\u51fa\u51fd\u6570y=f(x)\u7684\u56fe\u8c61\uff0c\u627e\u5230\u51fd\u6570\u56fe\u8c61\u4e0eX\u8f74\u7684\u4ea4\u70b9x ,x ,x ,\u2026\u2026x \uff0c\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3af(x)= f(x)=(x-x )(x-x )(x-x )\u2026\u2026(x-x )
\u4f8b9\u3001\u56e0\u5f0f\u5206\u89e3x +2x -5x-6
\u89e3\uff1a\u4ee4y= x +2x -5x-6
\u4f5c\u51fa\u5176\u56fe\u8c61\uff0c\u89c1\u53f3\u56fe\uff0c\u4e0ex\u8f74\u4ea4\u70b9\u4e3a-3\uff0c-1\uff0c2
\u5219x +2x -5x-6=(x+1)(x+3)(x-2)
10\u3001 \u4e3b\u5143\u6cd5
\u5148\u9009\u5b9a\u4e00\u4e2a\u5b57\u6bcd\u4e3a\u4e3b\u5143\uff0c\u7136\u540e\u628a\u5404\u9879\u6309\u8fd9\u4e2a\u5b57\u6bcd\u6b21\u6570\u4ece\u9ad8\u5230\u4f4e\u6392\u5217\uff0c\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b10\u3001\u5206\u89e3\u56e0\u5f0fa (b-c)+b (c-a)+c (a-b)
\u5206\u6790\uff1a\u6b64\u9898\u53ef\u9009\u5b9aa\u4e3a\u4e3b\u5143\uff0c\u5c06\u5176\u6309\u6b21\u6570\u4ece\u9ad8\u5230\u4f4e\u6392\u5217
\u89e3\uff1aa (b-c)+b (c-a)+c (a-b)=a (b-c)-a(b -c )+(b c-c b)
=(b-c) [a -a(b+c)+bc]
=(b-c)(a-b)(a-c)
11\u3001 \u5229\u7528\u7279\u6b8a\u503c\u6cd5
\u5c062\u621610\u4ee3\u5165x\uff0c\u6c42\u51fa\u6570P\uff0c\u5c06\u6570P\u5206\u89e3\u8d28\u56e0\u6570\uff0c\u5c06\u8d28\u56e0\u6570\u9002\u5f53\u7684\u7ec4\u5408\uff0c\u5e76\u5c06\u7ec4\u5408\u540e\u7684\u6bcf\u4e00\u4e2a\u56e0\u6570\u5199\u62102\u621610\u7684\u548c\u4e0e\u5dee\u7684\u5f62\u5f0f\uff0c\u5c062\u621610\u8fd8\u539f\u6210x\uff0c\u5373\u5f97\u56e0\u5f0f\u5206\u89e3\u5f0f\u3002
\u4f8b11\u3001\u5206\u89e3\u56e0\u5f0fx +9x +23x+15
\u89e3\uff1a\u4ee4x=2\uff0c\u5219x +9x +23x+15=8+36+46+15=105
\u5c06105\u5206\u89e3\u62103\u4e2a\u8d28\u56e0\u6570\u7684\u79ef\uff0c\u5373105=3\u00d75\u00d77
\u6ce8\u610f\u5230\u591a\u9879\u5f0f\u4e2d\u6700\u9ad8\u9879\u7684\u7cfb\u6570\u4e3a1\uff0c\u800c3\u30015\u30017\u5206\u522b\u4e3ax+1\uff0cx+3\uff0cx+5\uff0c\u5728x=2\u65f6\u7684\u503c
\u5219x +9x +23x+15=\uff08x+1\uff09\uff08x+3\uff09\uff08x+5\uff09
12\u3001\u5f85\u5b9a\u7cfb\u6570\u6cd5
\u9996\u5148\u5224\u65ad\u51fa\u5206\u89e3\u56e0\u5f0f\u7684\u5f62\u5f0f\uff0c\u7136\u540e\u8bbe\u51fa\u76f8\u5e94\u6574\u5f0f\u7684\u5b57\u6bcd\u7cfb\u6570\uff0c\u6c42\u51fa\u5b57\u6bcd\u7cfb\u6570\uff0c\u4ece\u800c\u628a\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b12\u3001\u5206\u89e3\u56e0\u5f0fx -x -5x -6x-4
\u5206\u6790\uff1a\u6613\u77e5\u8fd9\u4e2a\u591a\u9879\u5f0f\u6ca1\u6709\u4e00\u6b21\u56e0\u5f0f\uff0c\u56e0\u800c\u53ea\u80fd\u5206\u89e3\u4e3a\u4e24\u4e2a\u4e8c\u6b21\u56e0\u5f0f\u3002
\u89e3\uff1a\u8bbex -x -5x -6x-4=(x +ax+b)(x +cx+d)
= x +(a+c)x +(ac+b+d)x +(ad+bc)x+bd
\u6240\u4ee5 \u89e3\u5f97
\u5219x -x -5x -6x-4 =(x +x+1)(x -2x-4)
ab³-4ab=ab(b²-4)=ab(b+2)(b-2)
2.
3x²y+12xy²+12y³
=3y(x²+4xy+4y²)
=3y(x+2y)²
3.
x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy(x-y)²
4.
12a⁴b²-27a²b⁴
=3a²b²(4a²-9b²)
=3a²b²(2a+3b)(2a-3b)
5.
x²-xy+xz-yz
=x(x-y)+z(x-y)
=(x-y)(x+z)
6.
x²-y²+xz+yz
=(x+y)(x-y)+z(x+y)
=(x+y)(x-y+z)
7.
x²-4xy+4y²-1
=(x-2y)²-1
=(x-2y+1)(x-2y-1)
8.
x²-y²-z²+2yz
=x²-(y²-2yz+z²)
=x²-(y-z)²
=(x+y-z)(x-y+z)
9.
m²-n²-2n-1
=m²-(n²+2n+1)
=m²-(n+1)²
=(m+n+1)(m-n-1)
10.
4-a²+2a-1
=4-(a²-2a+1)
=4-(a-1)²
=(2+a-1)(2-a+1)
=(a+1)(3-a)
11.
9a²-b²-4b-4
=9a²-(b²+4b+4)
=(3a)²-(b+2)²
=(3a+b+2)(3a-b-2)
12.
9的平方-2a-35 【？？什么意思？】
13.
(a+b)²+7(a+b)+6
=(a+b+1)(a+b+6)
14.
x²-5xy-6y²
=(x+y)(x-6y)
15.
(x²+2x)²-(x²+2x)-2
=(x²+2x+1)(x²+2x-2)
=(x+1)²(x²+2x-2)
如果不懂，请追问，祝学习愉快！
1．m2(p－q)－p＋q； 2．a(ab＋bc＋ac)－abc； 3．x4－2y4－2x3y＋xy3；
4．abc(a2＋b2＋c2)－a3bc＋2ab2c2； 5．a2(b－c)＋b2(c－a)＋c2(a－b)； 6．(x2－2x)2＋2x(x－2)＋1； 7．(x－y)2＋12(y－x)z＋36z2； 8．x2－4ax＋8ab－4b2；
9．(ax＋by)2＋(ay－bx)2＋2(ax＋by)(ay－bx)； 10．(1－a2)(1－b2)－(a2－1)2(b2－1)2； 11．(x＋1)2－9(x－1)2； 12．4a2b2－(a2＋b2－c2)2； 13．ab2－ac2＋4ac－4a； 14．x3n＋y3n； 15．(x＋y)3＋125； 16．(3m－2n)3＋(3m＋2n)3； 17．x6(x2－y2)＋y6(y2－x2)； 18．8(x＋y)3＋1；
19．(a＋b＋c)3－a3－b3－c3； 20．x2＋4xy＋3y2；
解答
1．(p－q)(m－1)(m＋1)．
http://wenku.baidu.com/view/d5cb58323968011ca30091ff.html
答案在此
绛旓細1锛庡椤瑰紡x2锛峺2, x2锛2xy锛媦2, x3锛峺3鐨勫叕鍥犲紡鏄 銆2锛庡～涓婇傚綋鐨勬暟鎴栧紡锛屼娇宸﹁竟鍙垎瑙ｄ负鍙宠竟鐨勭粨鏋滐細(1)9x2锛( )2锛(3x锛 )( 锛15 y), (2).5x2锛6xy锛8y2锛(x )( 锛4y).3锛庣煩褰㈢殑闈㈢Н涓6x2锛13x锛5 (x>0),鍏朵腑涓杈归暱涓2x锛1,鍒欏彟涓 銆4锛庢妸a2锛峚锛6鍒嗚В鍥犲紡锛...
绛旓細鎵鏈夐鐩兘鏄敤鍗佸瓧鐩镐箻娉曡繘琛鍥犲紡鍒嗚В銆杩囩▼濡備笅锛3銆20x²-43xy+14y²=锛4x-7y锛夛紙5x-2y锛4銆18x²-19x+5 =锛9x-5锛夛紙2x-1锛5銆6x²-13x+6 =锛3x-2y锛夛紙2x-3y锛6銆5x²+4xy-28y²=锛坸-2锛夛紙5x+14锛7銆-35m²n²+11mn+6 =-35...
绛旓細x2=18 (9)x^2+4x-252=0 绛旀锛歺1=14 x2=-18 (10)x^2-11x-102=0 绛旀锛歺1=17 x2=-6 (11)x^2+15x-54=0 绛旀锛歺1=-18 x2=3 (12)x^2+11x+18=0 绛旀锛歺1=-2 x2=-9 (13)x^2-9x+20=0 绛旀锛歺1=4 x2=5 (14)x^2+19x+90=0 绛旀锛歺1=-10 x2=-9 (15)...
绛旓細鍥炵瓟锛=-(x^4-x^2-12) =-(x2-4)(x^2+3) =-(x-2)(x+2)(x^2+3)
绛旓細2. 宸茬煡A+B=8锛屼笖A²-B²=18锛屽垯浠ｆ暟寮廇-2B=-5/8 3. 宸茬煡涓姝ｆ柟褰㈢殑闈㈢Н涓9蟺X²+6蟺X+蟺锛圶锛0锛夛紝鐜板湪瑕佺敾涓涓笌姝ゆ鏂瑰舰闈㈢Н鐩哥瓑鐨勫渾锛屽垯鍦嗙殑鍗婂緞搴斾负蟺(3x+1)/2 4. 3锛圓+B锛²-27C²=3(A+B-3C)(A+B+3C)5. 1-8锛圡-N...
绛旓細涓銆佺敤鍥犲紡鍒嗚В娉曡В涓嬪垪鏂圭▼ (1) 3x^2-12x=-12 3(x²-4x+4)=0 3(x-2)²=0 x=2 (2) 4x^2-144=0 4(x²-36锛=0 4(x+6)(x-6)=0 x=-6鎴杧=6 (3) 3x(x-1)=2(x-1)(3x-2)(x-1)=0 x=2/3鎴杧=1 (4) (2x-1)^2=(3-x)^2 [(2x-1)+...
绛旓細1.鍘熷紡=9x²+12xy+4y²-9x²+12xy =4y²2.鍘熷紡=[(a-4)(a+10)+3a+12]*2+a+4 =(a²+10a-4a-40+3a+12)*2+a+4 =(a²+9a-28)*2+a+4 =2a²+18a-56+a+4 =2a²+19a-52 ...
绛旓細(x+1)^4+(x^2-1)^2+(x-1)^4 =(x+1)^4+(x+1)^2(x-1)^2+(x-1)^4 =[(x+1)^4+2(x+1)^2(x-1)^2+(x-1)^4]-(x+1)^2(x-1)^2 =(x +1+x-1)^2-(x^2-1)^2 =(2x)^2-(x^2-1)^2 =(2x+(x^2-1))(2x-(x^2-1))=-(x^2+2x-1)(x^2-...
绛旓細(1)鍘熷紡=4ab-4a²-b²=-(4a²-4ab+b²)=-(2a-b)²(2)鍘熷紡=2a[(x-1)²-x]=2a(x²-2x+1-x)=2a(x²-3x+1)(3)鍘熷紡=(a-b)銆(3a+b)²-(a+3b)²銆=锛坅-b锛塠(3a+b+a+3b)(3a+b-a-3b)]=(a-b)(4a+4b)...
绛旓細1.ab³-4ab=ab(b²-4)=ab(b+2)(b-2)2.3x²y+12xy²+12y³=3y(x²+4xy+4y²)=3y(x+2y)²3.x³y-2x²y²+xy³=xy(x²-2xy+y²)=xy(x-y)²4.12a⁴b²-27a²b⁴...
