因式分解中三

(1) 15^3-(x-5)^3
=(15-x+5)(225+15(x-5)+(x-5)^2)
=(20-x)(225+15x-75+x^2-10x+25)
=(20-x)(175+5x+x^2)

(2) 54u^6.v^2+250u^3.v^5
=2u^3*v^2(27u^3+125v^3)
=2u^3*v^2(3u+5v)(9u^2-15uv+25v^2)
(3)x^3+y^3+(3x^2.y+3x.y^2
=(x+y)(x^2-xy+y^2) +3xy(x+y)
=(x+y)(x^2-xy+y^2+3xy)
=(x+y)(x^2+2xy+y^2)
=(x+y)^3

15^3-(x-5)^3
(15-(x-5))(15^2+15(x-5)+(x-5)^2)
(10-x)(225+15x-75+x^2-10x+25)
(20-x)(275+5x+x^2)
______________________
54u^6.v^2+250u^3.v^5
2u^3v^2(27u^3-125v^3)
2u^3v^2(3u-5v)(9u^2+15uv+25v^2)
___________________
x^3+y^3+(3x^2y+3xy^2)
(x+y)(x^2+xy+y^2)+3xy(x+y)
(x+y)(x^2+4xy+y^2)

2010-12-04 11:45:59 補充：
Correction:
x^3+y^3+(3x^2y+3xy^2)
(x+y)(x^2-xy+y^2)+3xy(x+y)
(x+y)(x^2+2xy+y^2)
(x+y)(x+y)^2
(x+y)^3