4:
1: \(9-\left(x-y\right)^2=3^2-\left(x-y\right)^2\)
\(=\left(3-x+y\right)\left(3+x-y\right)\)
2: (x-y)2-4
=(x-y)2-22
=(x-y-2)(x-y+2)
3: \(\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
4: \(\left(3x+1\right)^2-\left(x+1\right)^2\)
\(=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\)
\(=2x\left(4x+2\right)=4x\left(2x+1\right)\)
5: \(\left(x+y\right)^2-\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)\left(x+y-x+y\right)\)
\(=2x\cdot2y=4xy\)
6: \(\left(2xy+1\right)^2-\left(2x+y\right)^2\)
\(=\left(2xy+1-2x-y\right)\left(2xy+1+2x+y\right)\)
\(=\left[2x\left(y-1\right)-\left(y-1\right)\right]\left[2x\left(y+1\right)+\left(y+1\right)\right]\)
\(=\left(y-1\right)\left(2x-1\right)\left(y+1\right)\left(2x+1\right)\)
7: \(9\left(x-y\right)^2-4\left(x+y\right)^2\)
\(=\left(3x-3y\right)^2-\left(2x+2y\right)^2\)
\(=\left(3x-3y-2x-2y\right)\left(3x-3y+2x+2y\right)\)
\(=\left(x-5y\right)\left(5x-y\right)\)
8: \(=\left(3x-2y-2x+3y\right)\left(3x-2y+2x-3y\right)\)
\(=\left(x-y\right)\left(5x-5y\right)\)
\(=5\left(x-y\right)^2\)
9: \(=4x^2-4x+1-x^2-2x-1\)
\(=3x^2-6x=3x\left(x-2\right)\)