因式分解：

(1)16x^3-24x^2y^2+12xy^4-2y^6
=2(8x^3-12x^2y^2+6xy^4-y^6)
=2(8x^3-4x^2y^2-8x^2y^2+4xy^4+2xy^4-y^6)
=2[4x^2(2x-y^2)-4xy^2(2x-y^2)+y^4(2x-y^2)]
=2(2x-y^2)(4x^2-4xy^2+y^4)
=2(2x-y^2)(2x-y^2)^2
=2(2x-y^2)^3
(2)a^3+3a^2b+3b^2a-7b^3
=a^3-a^2b+4a^2b-4b^2a+7b^2a-7b^3
=a^2(a-b)+4ab(a-b)+7b^2(a-b)
=(a-b)(a^2+4ab+7b^2)实数范围分解到此结束
=(a-b)(a^2+4ab+4b^2+3b^2)
=(a-b)[(a+2b)^2+3b^2]
=(a-b)(a+2b+√3ib)(a+2b-√3ib)
(3)2(a^2+b^2)(a+b)^2-(a^2-b^2)^2
=2(a^2+b^2)(a+b)^2-(a+b)^2(a-b)^2
=(a+b)^2[2(a^2+b^2)-(a-b)^2]
=(a+b)^2[2a^2+2b^2-a^2+2ab-b^2]
=(a+b)^2(a^2+b^2+2ab)
=(a+b)^2(a+b)^2
=(a+b)^4
(4)(x^2+y^2)^3+(z^2-x^2)^3-(y^2+z^2)^3
=(x^2+y^2)^3+[(z^2-x^2)-(y^2+z^2)][(z^2-x^2)^2+(z^2-x^2)(y^2+z^2)+(y^2+z^2)^2]
=(x^2+y^2)^3+[z^2-x^2-y^2-z^2][(z^4-2z^2x^2+x^4)+(z^4-x^2y^2+y^2z^2-x^2z^2)+(y^4+2y^2z^2+z^4)]
=(x^2+y^2)^3+(-x^2-y^2)[z^4-2z^2x^2+x^4+z^4-x^2y^2+y^2z^2-x^2z^2+y^4+2y^2z^2+z^4]
=(x^2+y^2)^3-(x^2+y^2)[3z^4-3z^2x^2+3y^2z^2+x^4-x^2y^2+y^4]
=(x^2+y^2)[(x^2+y^2)^2-(3z^4-3z^2x^2+3y^2z^2+x^4-x^2y^2+y^4)
=(x^2+y^2)[(x^4+2x^2y^2+y^4-3z^4+3z^2x^2-3y^2z^2-x^4+x^2y^2-y^4)
=(x^2+y^2)(3x^2y^2-3z^4+3z^2x^2-3y^2z^2)
=3(x^2+y^2)(x^2y^2-z^4+z^2x^2-y^2z^2)
=3(x^2+y^2)(x^2y^2+z^2x^2-y^2z^2-z^4)
=3(x^2+y^2)[x^2(y^2+z^2)-z^2(y^2+z^2)]
=3(x^2+y^2)(y^2+z^2)(x^2-z^2)
=3(x^2+y^2)(y^2+z^2)(x+z)(x-z)
(5)x^2+9y^2+4z^2-6xy+4xz-12yz
=(x-3y+2z)^2
(6)a^2-b^2-3c^2-2ac+4bc
=a^2-2ac+c^2-b^2-4c^2+4bc
=(a-c)^2-(b-2c)^2
=(a-c+b-2c)(a-c-b+2c)
=(a+b-3c)(a-b+c)
(7)x^4+y^4+(x+y)^4
=x^4+y^4+x^4+4x^3y+6x^2y^2+4xy^3+y^4
=2x^4+4x^3y+6x^2y^2+4xy^3+2y^4
=2(x^4+2x^3y+3x^2y^2+2xy^3+y^4)
=2(x^4+x^2y^2+y^4+2x^3y+2x^2y^2+2xy^3)
=2(x^2+xy+y^2)^2

（1）16x^3-24x^2y^2+12xy^4-2y^6=2(2x)^3-2y^6-12xy^2(2x-y^2)=2(2x-y^2)(4x^2+2xy^2+y^4)-12xy^2(2x-y^2)=2(2x-y^2)(4x^2-4xy^2+y^4)=2(2x-y^2)(2x-y^2)^2=2(2x-y^2)^3

(2)a^3+3a^2b+3b^2a-7b^3=a^3+3a^2b+3b^2a+b^3-8b^3=(a+b)^3-(2b)^3=(a-b)(a^2+4ab+7b^2)

(3)2(a^2+b^2)(a+b)^2-(a^2-b^2)^2=2(a^2+b^2)(a+b)^2-(a+b)^2(a-b)^2=(a+b)^2(2a^2+2b^2-a^2+2ab-b^2)=(a+b)^2(a+b)^2=(a+b)^4

(4)(x^2+y^2)^3+(z^2-x^2)^3-(y^2+z^2)^3=(x^2+y^2-y^2-z^2)((x^2+y^2)^2+(x^2+y^2)(y^2+z^2)+(y^2+z^2)^2)-(x^2-z^2)(x^4+x^2z^2+z^4)=(x^2-z^2)(3y^4+3x^2y^2+3y^2z^2)=3y^2(x^2-z^2)(x^2+y^2+z^2)

(5)x^2+9y^2+4z^2-6xy+4xz-12yz=(x-3y)^2-4z(x-3y)+4z^2=(x-3y-2z)^2

(6)a^2-b^2-3c^2-2ac+4bc=a^2-2ac+c^2-b^2+4bc-4c^2=(a-c)^2-(b-2c)^2=(a+b-3c)(a-b+c)

(7)x^4+y^4+(x+y)^4=(x^2+y^2)^2-2x^2y^2+(x+y)^4=(x+y)^2(x-y)^2+(x+y)^4=(x+y)^2((x-y)^2+(x-y)^2)=(x+y)^2*2(x^2+y^2)=2(x+y)^2(x^2+y^2)