因式分解(請快)

a^3 - b^3 + 3ab^2 - 3a^2b
= a^3 - 3a^2b + 3ab^2 - b^3
= (a - b)^3


x^6 + 2x^4y^2 + y^4x^2 - 4
= (x^4 + 2x^2y^2 + y^4)x^2 - 4
= (x^2 + y^2)^2 x^2 - 4
= [(x^2 + y^2) x]^2 - 2^2
= [(x^2 + y^2) x - 2] [(x^2 + y^2) x + 2]
= (x^3 + y^2 x - 2) (x^3 + y^2 x + 2)

a^3-b^3+3ab^2-3a^2b

=(a-b)(a^2+ab+b^2)+3ab^2-3a^2b----------恆等式:a^3-b^3=(a-b)(a^2+ab+b^2)

=(a-b)(a^2+ab+b^2)+3ab(b-a)----------------因式分解

=(a-b)(a^2+ab+b^2)-3ab(a-b)-----------------抽負

=(a-b)(a^2+ab+b^2)-3ab

x^6+2x^4y^2+y^4x^2-4

=x^6+(2x^4 y^2)+(y^4 x^2)-4

=(y^4 x^2)+x^6+(2x^4 y^2)-4----------------排列好

=[x^2(y^4+x^4)+2(x^4 y^2-2)]--------------因式分解

=x^4y^2[(x^2(y^2+1))+2(1-2)]

=x^4y^2[(x^2(y^2+1)-2]

唔知對不對ne?

2007-11-03 18:49:35 補充：
a³-b³+3ab²-3a²b=a³-3a²b+3ab²-b³----------------排列好 =(a-b)^3-----------------------------利用恆等式:a³-3a²b+3ab²-b³=(a-b)^3

2007-11-03 18:49:45 補充：
x^6+2x^4(y²)+y^4(x²)-4 =x²(x^4+2x²y²+y^4)-4--------------------因式分解=x²(x²+y²)²-4--------------------------------先十字相乘,再因式分解= [(x²+y²)x]² - 2^2= [(x²+y²)x-2][(x²+y²)x+2]= (x³+y²x-2)(x³+y²x+2)