数学代数证明1.a+b+c=0②a4+b4+c4=2a2b2+2b2c2+2c2a2（后面的4和2都是次方）2.(x-2

(1)a^4+b^4+c^4
=(a^2+b^2+c^2)^2-2(a^2b^2+b^2c^2+c^2a^2)
=[(a+b+c)^2-2(ab+bc+ca)]^2-2(a^2b^2+b^2c^2+c^2a^2)
=4(ab+bc+ca)^2-2(a^2b^2+b^2c^2+c^2a^2)
=4[a^2b^2+b^2c^2+c^2a^2+2abc(a+b+c)]-2(a^2b^2+b^2c^2+c^2a^2)
=4(a^2b^2+b^2c^2+c^2a^2)-2(a^2b^2+b^2c^2+c^2a^2)
=2(a^2b^2+b^2c^2+c^2a^2)
(2)(x-2y)x^3-(y-2x)y^3
=x^4-y^4-2yx^3+2xy^3
=(x^2-y^2)(x^2+y^2)-2xy(x^2-y^2)
=(x^2-y^2)(x^2+y^2-2xy)
=(x+y)(x-y)(x-y)^2
=(x+y)(x-y)^3