因式分解 x^3 + y^3 + 3xy - 1
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ej0cl6

2006-02-05 21:28
x^3+y^3+3xy-1
=(x+y)^3-3xy(x+y)+3xy-1
=(x+y-1)(x^2+2xy+y^2+x+y+1)-3xy(x+y-1)
=(x+y-1)(x^2-xy+y^2+x+y+1)

aa963854116

2006-02-06 09:28
利用a^3+b^3+c^3-3abc
=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
取a=x,b=y,c=-1即可
這是一個好用的公式

kc81731

2006-02-06 11:25
x^3+y^3+3xy-1
=(x+y)^3-3xy(x+y)+3xy-1
=(x+y-1)(x^2+2xy+y^2+x+y+1)-3xy(x+y-1)
=(x+y-1)(x^2-xy+y^2+x+y+1)

qqwwee2006

2006-02-23 22:48
答案....(x+y-1)(x^2-xy+y^2+x+y+1)

mathematical2005

2006-02-24 00:02
x^3+y^3+3xy-1
=(x+y)^3-3xy(x+y)+3xy-1
=(x+y-1)(x^2+2xy+y^2+x+y+1)-3xy(x+y-1)
=(x+y-1)(x^2-xy+y^2+x+y+1)

訪客 (未驗證)

2006-02-28 17:54
(x+y-1)(x^2-xy+y^2+x+y+1)