\(1,9-\left(x-y\right)^2=\left(3+x-y\right)\left(3-x+y\right)\\ 2,\left(x-y\right)^2-4\\=\left(x-y+2\right)\left(x-y-2\right)\\ 3,\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\\ 4,\left(3x+1\right)^2-\left(x+1\right)^2=\left(2x\right)\left(4x+2\right)\\ 5,\left(x+y\right)^2-\left(x-y\right)^2=2x\cdot2y=4xy\)
\(6,\left(2xy+1\right)^2-\left(2x+y\right)^2=\left(2x+y+2xy+1\right)\left(2xy+1-2x-y\right)=\left(2x+1\right)\left(y+1\right)\left(2x-1\right)\left(y-1\right)\\ 7,9\left(x-y\right)^2-4\left(x+y\right)^2=\left(3x-3y+2x+2y\right)\left(3x-3y-2x-2y\right)=\left(5x-y\right)\left(x-5y\right)\\ 8,\left(3x-2y\right)^2-\left(2x-3y\right)^2=\left(5x-5y\right)\left(x+y\right)\\ 9,\left(4x^2-4x+1\right)-\left(x+1\right)^2=\left(2x-1\right)^2-\left(x+1\right)^2=\left(3x\right)\left(x-2\right)\)
1: =3^2-(x-y)^2
=(3-x+y)(3+x-y)
2: (x-y)^2-4
=(x-y)^2-2^2
=(x-y-2)(x-y+2)
3: =(x+2)^2-y^2
=(x+2-y)(x+2+y)
4: =(3x+1-x-1)(3x+1+x+1)
=(2x)*(4x+2)
=4x(2x+1)
5: =(x+y-x+y)(x+y+x-y)
=2x*2y
=4xy
6: =(2xy+1-2x-y)(2xy+1+2x+y)
=[2x(y-1)-(y-1)]*[2x(y+1)+(y+1)]
=(y-1)(2x-1)(y+1)(2x+1)
7: =[3*(x-y)]^2-[2(x+y)]^2
=(3x-3y)^2-(2x+2y)^2
=(3x-3y-2x-2y)(3x-3y+2x+2y)
=(x-5y)(5x-y)
8: =(3x-2y-2x+3y)(3x-2y+2x-3y)
=(5x-5y)(x+y)
=5(x-y)(x+y)
9: =(2x-1)^2-(x+1)^2
=(2x-1+x+1)(2x-1-x-1)
=(x-2)*3x