解1：
(2x^2)^3-6(x^3)(x^3+2x^2+x)
=8x^6-6x^6-12x^5-6x^4
=2x^6-12x^5-6x^4
解2：
(x+y+z)(x+y-z)
=(x+y)(x+y-z)+z(x+y-z)
=x(x+y-z)+y(x+y-z)+z(x+y-z)
=x^2+xy-xz+xy+y^2-yz+xz+yz-z^2
=x^2+3xy-xz+y^2-z^2
=x^2+y^2-z^2+3xy-xz
解3：
[(x+y)^2-(x-y)^2]÷(2xy)
=[(x+y)+(x-y)][(x+y)-(x-y)]×[1/(2xy)]
=(x+y+x-y)(x+y-x+y)/(2xy)
=2x×2y/(2xy)
=4xy/(2xy)
=2
解4：
(a^2)(a+1)^2-2(a^2-2a+4)
=(a^2)(a^2+2a+1)-(2a^2-4a+8)
=a^4+2a^3+a^2-2a^2+4a-8
=a^4+2a^3-a^2+4a-8