3x(2x+y)²-12x(x+2y)²

3x(2x+y)²-12x(x+2y)²
=3x[(2x+y)²-4(x+2y)²]
=3x(2x+y+2x+4y)(2x+y-2x-4y)
=3x(4x+5y)(-3y)
=-9xy(4x+5y)

3x[(2x+y)²-4(x+2y)²]
=3x{[(2x+y)+2(x+2y)][(2x+y)-2(x+2y)]}
=3x(4x+5y)(-3y)
=-9xy(4x+5y)
=-36x²y-45xy²
不知道你是需要什么结果……
不过一般就只能到这步了……

3x(2x+y)²-12x(x+2y)²
=3x(4x^2+4xy+y^2)-12x(x^2+4xy+4y^2)
=12x^3+12x^2y+3xy^2-12x^3-48x^2y-48xy^2
=-36x^y-45xy^2