1.(2x-3y)^2-(y+3x)(3x-y)
=4x^2-12xy+9y^2-(3x+y)(3x-y)
=4x^2-12xy+9y^2-9x^2+y^2
=10y^2-5x^2-12xy
2.[(x-y)^2+(x+y)^2](x^2-y^2)
=[x^2-2xy+y^2+x^2+2xy+y^2](x^2-y^2)
=2(x^2+y^2)(x^2-y^2)
=2x^4-2y^4
3.(-1/2)^0+(-2)^3+(1/3)^-1+2
=1-8+3+2
=-2
4.(3x+2y)^2(3x-2y)^2
=[(3x+2y)(3x-2y)]^2
=(9x^2-4y^2)^2
=81x^4-72x^2y^2+16y^4
5.-8a^3b^2+12ab^3c-6a^2b
=-2ab(4a^2b-6bc+3a)
6.x^3-2x^2+x
=x(x^2-2x+1)
=x(x-1)^2
7.2a(x^2+1)^2-8ax^2
=2a[(x^2+1)^2-4x^2]
=2a(x^2+1-2x)(x^2+1+2x)
=2a(x-1)^2(x+1)^2