1. (-2/3x-3/2y)²=(-2/3x)²+2(-2/3x)(-3/2y)+(-3/2y)²=4/9x²+2xy+9/4y²
2. x²-(x+2)(x-2)-(x+1/x)²=x²-(x²-4)-(x²+2+1/x²)=x²-x²+4-x²-2-1/x²=-x²+2-1/x²=-(x-1/x)²
3. [(x+y)²-(x-y)²]/(2xy)= [x²+2xy+y²-(x²-2xy+y²)]/(2xy)=[2xy+2xy]/(2xy)=2
4. 3x-12x³ =3x(1-4x²)=3x(1-2x)(1+2x)
5. -2a³+12a²-18a= -2a(a²-6a+9)=-2a(a-3)²
6. 9a²(x-y)+4b²(y-x) = 9a²(x-y)-4b²(x-y)=(9a²-4b²) (x-y)=(3a-2b)(3a+2b)(x-y)
7.(x+y)²+2(x+y)+1=(x+y+1)²