关于因式分解.我真的很急.明天就要.求你们了!1.(x-y)^5+(y-Z)^5+(z-x)^5=2.(a+b)^5-a^5-b^5=

Question

关于因式分解.我真的很急.明天就要.求你们了!
1.(x-y)^5+(y-Z)^5+(z-x)^5=
2.(a+b)^5-a^5-b^5=

Answer 1

(x-y)^5+(y-z)^5+(z-x)^5
=(x-y)^5+(y-z)^5+{-[(x-y)+(y-z)]}^5
=(x-y)^5+(y-z)^5-[(x-y)+(y-z)]^5
=(x-y)^5+(y-z)^5-[(x-y)^5+5(x-y)^4(y-z)+10(x-y)^3(y-z)^2+10(x-y)^2(y-z)^3+5(x-y)(y-z)^4+(y-z)^5]
=(x-y)^5+(y-z)^5-(x-y)^5-(y-z)^5-[5(x-y)^4(y-z)+10(x-y)^3(y-z)^2+10(x-y)^2(y-z)^3+5(x-y)(y-z)^4]
=-[5(x-y)^4(y-z)+10(x-y)^3(y-z)^2+10(x-y)^2(y-z)^3+5(x-y)(y-z)^4]
=-5[(x-y)^4(y-z)+2(x-y)^3(y-z)^2+2(x-y)^2(y-z)^3+(x-y)(y-z)^4]
=-5[(x-y)^4(y-z)+(x-y)(y-z)^4+2(x-y)^3(y-z)^2+2(x-y)^2(y-z)^3]
=-5(x-y)(y-z)[(x-y)^3+(y-z)^3+2(x-y)^2(y-z)+2(x-y)(y-z)^2]
=-5(x-y)(y-z)[(x-y)^3+(x-y)^2(y-z)+(y-z)^3+(x-y)(y-z)^2+(x-y)^2(y-z)+(x-y)(y-z)^2]
=-5(x-y)(y-z){(x-y)^2[(x-y)+(y-z)]+(y-z)^2[(x-y)+(y-z)]+(x-y)(y-z)[(x-y)+(y-z)]}
=-5(x-y)(y-z)[(x-y)+(y-z)][(x-y)^2+(y-z)^2+(x-y)(y-z)]
=-5(x-y)(y-z)(x-z)[(x-y)^2+(y-z)^2+(x-y)(y-z)]
=-5(x-y)(y-z)(x-z)[(x^2-2xy+y^2+y^2-2yz+z^2+xy-xz-y^2+yz)]
=5(x-y)(y-z)(z-x)[(x^2-2xy+y^2+y^2-2yz+z^2+xy-xz-y^2+yz)]
=5(x-y)(y-z)(z-x)[(x^2+y^2+y^2-y^2+z^2+xy-2xy-xz+yz-2yz)]
=5(x-y)(y-z)(z-x)(x^2+y^2+z^2-xy-xz-yz)
(a＋b)^5－a^5－b^5
=5a^4b+10a^3b^2+10a^2b^3+5ab^4
=5ab(a^3+2a^2b+2ab^2+b^3)
=5ab[(a^3+b^3)+2ab(a+b)]
=5ab[(a+b)(a^2-ab+b^2)+2ab(a+b)]
=5ab(a+b)(a^2-ab+b^2+2ab)
=5ab(a+b)(a^2+ab+b^2)