9道因式分解的题目。。。
9\u9053\u56e0\u5f0f\u5206\u89e3\u98981\uff09(x+y)^3+2xy(1-x-y)-1
\u7acb\u65b9\u5dee\u516c\u5f0f\uff1aa³-b³=(a-b)(a²+ab+b²)
(x+y)^3+2xy(1-x-y)-1
=[(x+y)³-1]-2xy(x+y-1)
=(x+y-1)[(x+y)²+(x+y)+1]- 2xy(x+y-1)
=(x+y-1)(x²+y²+x+y+1)
2\uff09x^3+x^2-2004*2005x
=x\uff08x²+x-2004\u00d72005\uff09
=x\uff08x+2005\uff09\uff08x-2004\uff09
3\uff09(x^2-x-6)(x^2+3x-4)+24
=(x-3)(x+2)(x+4)(x-1)+24
=[(x-3)(x+4)][(x+2)(x-1)]+24
=(x²+x-12)(x²+x-2)+24
=[(x²+x)-12][(x²+x)-2]+24
=(x²+x)²-14(x²+x)+24+24
=(x²+x)²-14(x²+x)+48
=(x²+x-6)(x²+x-8)
=(x+3)(x-2)(x²+x-8\uff09
4\uff09x^6+15x^3y+50y^2
\u8bbex³=a\uff0c
\u539f\u5f0f
=a²+15ay+50y²
=(a+10y)(a+5y)
\u518d\u4ee3\u56de\u53bb
=(x³+10y)(x³+5y)
5\uff09\uff08x^2+4x+6\uff09+(x^2+6x+6)+x^2
\u8bbex²+5x+6=a
\u539f\u5f0f
=(a-x)(a+x)+x²
=a²
=(x²+5x+6)²
=(x+3)²(x+2)
6\uff09(x-3)(x+4)(x-5)(x+6)+80
(x-3)(x+4)(x-5)(x+6)+80
=(x-3)(x+4)(x-5)(x+6)+80
=(x²-x-12)(x²-x-30)+80
=[(x²-x)-12][(x²-x)-30]+80
=(x²-x)²-42(x²-x)+360+80
=(x²-x)²-42(x²-x)+440
=(x²-x-20)(x²-x-22)
=(x-5)(x+4)(x²-x-22)
7\uff09x^3-7x+6
=x³-x²+x²-x-6x+6
=(x³-x²)+(x²-x)-(6x-6)
=x²(x-1)+x(x-1)-6(x-1)
=(x-1)(x²+x-6)
=(x-1)(x+3)(x-2)
8\uff09x^4+y^4+(x+y)^4
=(x²+y²)²-2x²y²+(x+y)^4
=[(x+y)²-2xy]²-2x²y²+(x+y)^4
=(x+y)^4-4xy(x+y)²+4x²y²-2x²y²+(x+y)^4
=2(x+y)^4-4xy(x+y)²+2x²y²
=2\u3010[(x+y)²]²-2xy(x+y)²+(xy)²\u3011
=2[(x+y)²-xy]²
=2(x²+xy+y²)²
9\uff09xy(xy+1)+(xy+3)-2(x+y+1/2)-(x+y-1)^2
=x²y²+xy+xy+3-2(x+y)-1-[(x+y)²-2(x+y)+1]
=[x²y²+2xy+1]-2(x+y)+1-(x+y)²+2(x+y)-1
=(xy+1)²-(x+y)²
=(xy-x-y+1)(xy+x+y+1)
=[x(y-1)-(y-1)][y(x+1)+(y+1)]
=(x-1)(x+1)(y+1)(y-1)
\u3010\u5e0c\u671b\u5bf9\u4f60\u6709\u5e2e\u52a9\u3011
X^6-1=\uff08x^3+1)(x^3-1\uff09
\u2235x^3+1=\uff08x+1\uff09\uff08x^2+x+1)
x^3-1=\uff08x-1\uff09\uff08x^2+x+1)
\u2234=\uff08x+1\uff09\uff08x^2+x+1)\uff08x-1\uff09\uff08x^2+x+1)
\u5e94\u8be5\u662f\u7684\u5427\u3002\u3002\u516c\u5f0f\u90a3\u4e2a\u6211\u4eec\u8fd8\u6ca1\u5b66\uff0c\u6211\u662f\u7f51\u4e0a\u67e5\u7684\uff0c\u81ea\u5df1\u6f14\u7b97\u4e5f\u7b97\u5f97\u56de\u53bb\u3002
\u518d\u52a0\u4e2a\u63a8\u5bfc\u8fc7\u7a0b\u5427\u3002
x^3-1
=x³-x²+x²-x+x-1
=x²(x-1)+x(x-1)+(x-1)
=(x-1)(x²+x+1)
x^3+1\u7684\u63a8\u5bfc\u5927\u81f4\u5dee\u4e0d\u591a
\u540c\u6837\u4e5f\u53ef\u4ee5\u7528\u7acb\u4f53\u56fe\u5f62\u6765\u89e3\u91ca\uff0c
x^3-1\uff1a
\u4e00\u4e2a\u8fb9\u957f\u4e3ax\u7684\u6b63\u65b9\u4f53\uff0c\u4e00\u4e2a\u68f1\u89d2\u90e8\u4f4d\u51cf\u53bb\u4e00\u4e2a\u8fb9\u957f\u4e3a1\u7684\u5c0f\u6b63\u65b9\u4f53
\u8fd9\u5206\u5272\u6210\u4e3a\u4e09\u4e2a\u957f\u65b9\u4f53\uff1a1²\u00d7\uff08x-1\uff09 1\u00d7\uff08x-1\uff09\u00d7X x²\u00d7\uff08x-1\uff09
\u5c06\u4e0a\u9762\u90a3\u4e09\u4e2a\u5f0f\u5b50\u76f8\u52a0\u5e76\u5316\u7b80\uff1a1²\u00d7\uff08x-1\uff09\uff0b 1\u00d7\uff08x-1\uff09\u00d7X+ x²\u00d7\uff08x-1\uff09
=\uff08x-1\uff09\uff081+x+x²\uff09
\u2234x^3-1=\uff08x-1\uff09\uff081+x+x²\uff09
\u540cx^3-1\uff0c\u5219x^3+1\u4e3a\uff1a
\u4e00\u4e2a\u8fb9\u957f\u4e3ax\u7684\u6b63\u65b9\u4f53\uff0c\u4e00\u4e2a\u68f1\u89d2\u90e8\u4f4d\u52a0\u4e0a\u4e00\u4e2a\u8fb9\u957f\u4e3a1\u7684\u5c0f\u6b63\u65b9\u4f53\uff0c\u4f7f\u5c0f\u6b63\u65b9\u4f53\u7684\u4e24\u6761\u76f8\u90bb\u5e95\u8fb9\u4e0e\u5927\u6b63\u65b9\u4f53\u7684\u4e24\u6761\u76f8\u90bb\u5e95\u8fb9\u76f8\u63a5
\u540c\u6837\u5206\u5272\u6210\u4e09\u4e2a\u957f\u65b9\u4f53\uff1a1²\u00d7\uff08x\uff0b1\uff09 1\u00d7\uff08x-1\uff09\u00d7X x²\u00d7\uff08x-1\uff09
\u76f8\u52a0\u5e76\u7b80\u5316\uff1a1²\u00d7\uff08x+1\uff09\uff0b 1\u00d7\uff08x-1\uff09\u00d7X+ x²\u00d7\uff08x-1\uff09
=\uff08x+1\uff09\uff08x²+x+1)
=(a+b)x²-(a²+2ab+b²)x+a²b+ab²
=(a+b)[x²-(a+b)x+ab]
=(a+b)(x-a)(x-b)
（2）（a+b-2ab）(a+b-2)+(1-ab)² 令a+b=x ，ab=y
原式=(x-2y)(x-2)+(1-y)²
=x²-2x-2xy+4y+y²-2y+1
=x²-2x-2xy+2y+y²+1
=(x-y)²-2(x-y)+1
=(x-y-1)²
=(a+b-ab-1)²
=(a-1)²(b-1)²
（3）（1+y）²-2x²（1+y²）+x⁴（1-y）²
=（1-y）²x⁴-2（1+y²）x²+(1+y）²
=[(1-y)²x²-(1+y)²](x²-1)
=(x-xy+1+y)(x-xy-1-y)(x+1)(x-1)
（4）x⁴-6x²-7x-6
=x⁴-3x³+3x³-9x²+3x²-7x-6
=x³(x-3)+3x²(x-3)+(3x+2)(x-3)
=(x-3)(x³+3x²+3x+2)
=(x-3)[x²(x+2)+(x+2)(x+1)]
=(x-3)(x+2)(x²+x+1)
（5）x⁴+x³-2x²-4x-4
设f(x)=x⁴+x³-2x²-4x-4
f(1)=-8,f(2)=4,f(3)=74
（6）（m²+7m-12）（m²+7m+4）-13²
设a=m²+7m
原式=a²-8a-217,用求根公式分解,怀疑数据有问题
（7）（x²-1）（x²+8x+15）+15
=x⁴+8x³+15x²-x²-8x-15+15
=x⁴+8x³+14x²-8x
=x(x³+8x²+14x-8)
=x(x³+8x²+16x-2x-8)
=x[x(x+4)²-2(x+4)]
=x(x+4)(x²+4x-2)
=x(x+4)(x+2+√6)(x+2-√6)
（8）（1-a²）（1-b²）-4ab
=1-a²-b²+a²b²-4ab
=(ab-1)²-(a+b)²
=(ab-1+a+b)(ab-1-a-b)
（9）求x的平方-y的平方-29=0整数解
x²-y²=29
(x+y)(x-y)=1×29=(-1)×(-29)
得到4个方程组
①x+y=29,x-y=1
x=15,y=14
②x+y=1,x-y=29
x=15,y=-14
③x+y=-29,x-y=-1
x=-15,y=-14
④x+y=-1,x-1=-29
x=-15,y=14
解：⑴原式＝(a+b)x^2-(a^2+2ab+b^2)x+a^2b+ab^2
=(a+b)x^2-(a+b)^2x+ab(a+b)=(a+b)[x^2-(a+b)x+ab]=(a+b)(x-a)(x-b)
⑵令a+b=x ，ab=y则
原式＝(x-2y)(x-2)+(1-y)^2=x^2-2xy+y^2-2x+2y+1
=(x-y)^2-2(x-y)+1=(x-y-1)^2
将x=a+b，y=ab代入上式得
原式＝(a+b-ab-1)^2=(a-1)^2*(b-1)^2
⑶用十字相乘法分解得
原式＝[(1-y)^2x^2-(1+y)^2](x^2-1)=[(1-y)x+1+y][(1-y)x-1-y](x+1)(x-1)
=(x+y-xy+1)(x-y-xy-1)(x+1)(x-1)
⑷原式＝x^4-3x^3+3x^3-9x^2+3x^2-7x-6
=x^3(x-3)+3x^2(x-3)+(3x+2)(x-3)
=(x-3)(x^3+3x^2+3x+2)=(x-3)(x^3+2x^2+x^2+3x+2)
=(x-3)[x^2(x+2)+(x+1)(x+2)]=(x-3)(x+2)(x^2+x+1)
打字太费事了，等有时间再说
1 (a+b)(x-a)(x-b)
2 (1-b)的平方
3 （1+y=x四次方(1-y))平方
绛旓細1锛(x+y)^3+2xy(1-x-y)-1 绔嬫柟宸叕寮忥細a³-b³=(a-b)(a²+ab+b²)(x+y)^3+2xy(1-x-y)-1 =[(x+y)³-1]-2xy(x+y-1)=(x+y-1)[(x+y)²+(x+y)+1]- 2xy(x+y-1)=(x+y-1)(x²+y²+x+y+1)2锛墄^3+x^2-2004...
绛旓細1.锛坸+3锛夛紙x锛2锛2.锛2x锛3锛夛紙x+4锛3.锛5x-2锛夛紙x锛1锛4.锛2x+3锛夛紙x+2锛5.锛3x锛2锛夛紙x+5锛6.锛坸+3锛7.锛2x锛1锛夛紙x锛6锛8.(x锛4)(x锛2)9.锛2x锛3锛
绛旓細(1锛塧x²-a²x+bx²-2abx+a²b-b²x+ab²=(a+b)x²-(a²+2ab+b²)x+a²b+ab²=(a+b)[x²-(a+b)x+ab]=(a+b)(x-a)(x-b)锛2锛夛紙a+b-2ab锛(a+b-2)+(1-ab)² 浠+b=x 锛宎b=y 鍘...
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绛旓細=3^1998脳(3²-4脳3+10)=3^1998脳(9-12+10)=3^1998脳7 鑳借7鏁撮櫎 2.m²-4n²+4n-1 =m²-(4n²-4n+1)=m²-(2n-1)²=(m-2n+1)*(m+2n-1)3.x²-4y²+2x-4y =(x-2y)(x+2y)+2(x-2y)=(x-2y)(x+2y+2)4.x&...
绛旓細37.鍥犲紡鍒嗚Вx2锛4x锛3锛 銆38.鍥犲紡鍒嗚В4x2锛12x锛5锛 銆39.鍥犲紡鍒嗚В涓嬪垪鍚勫紡锛(1)3ax2锛6ax锛 銆(2)x(x锛2)锛峹锛 銆(3)x2锛4x锛峚x锛4a锛 銆(4)25x2锛49锛 銆(5)36x2锛60x锛25锛 銆(6)4x2锛12x锛9锛 銆(7)x2锛9x锛18锛 銆(8)2x2锛5x锛3锛 銆(9)12x2锛50x锛8...
绛旓細18銆4X^+12X+9=(2X+3)(2X+3)19銆5Y^2-7Y-6=(5Y+3)(Y-2)20銆2Y^2-Y-6=(2Y+3)(Y-2)21銆2X^2-XY-Y^2=(2X+Y)(X-Y)22銆6X^2-2XY-4Y^2=(3X+2Y)(2X-2Y)23銆5X^2-6XY+Y^2=(5X-Y)*(X-Y)24銆6X^2-7X+1=(6X-1)(X-1)25銆4Y^2-6Y+2=(4Y-2)(Y-1)...
绛旓細46.鍥犲紡鍒嗚В-20x2+9x+20= 銆47.鍥犲紡鍒嗚В12x2-29x+15= 銆48.鍥犲紡鍒嗚В36x2+39x+9= 銆49.鍥犲紡鍒嗚В21x2-31x-22= 銆50.鍥犲紡鍒嗚В9x4-35x2-4= 銆51.鍥犲紡鍒嗚В(2x+1)(x+1)+(2x+1)(x-3)= 銆52.鍥犲紡鍒嗚В2ax2-3x+2ax-3= 銆53.鍥犲紡鍒嗚Вx(y+2)-x-y-1= 銆54.鍥犲紡鍒嗚В(x2...
绛旓細5.鍥犲紡鍒嗚Вa^4锛9a^2b^2锛漚^2(a+3b)(a-3b)8.鍥犲紡鍒嗚Вab(x^2锛峺^2)锛媥y(a^2锛峛^2)锛(ay+bx)(ax-by)9.鍥犲紡鍒嗚В(x锛媦)(a锛峛锛峜)锛(x锛峺)(b锛媍锛峚)锛2y(a-b-c)10.鍥犲紡鍒嗚Вa^2锛峚锛峛^2锛峛锛(a+b)(a-b-1)11.鍥犲紡鍒嗚В(3a锛峛)2锛4(3a锛峛)(a锛3b)锛4(a...
绛旓細4.abc锛媋b锛4a锛漚(bc+b-4)5.16x2锛81锛(4x+9)(4x-9)6.9x2锛30x锛25锛(3x-5)^2 7.x2锛7x锛30锛(x-10)(x+3)8.x2锛25锛(x+5)(x-5)9.x2锛20x锛100锛(x-10)^2 10.x2锛4x锛3锛(x+1)(x+3)11.4x2锛12x锛5锛(2x-1)(2x-5)12.3ax2锛6ax锛3ax(x-2)13....
