1: \(x^2-2x+1-y^2+2x-1\)
\(=x^2-y^2\)
=(x-y)(x+y)
3: \(4x^2-4x+1-y^2-8y-16\)
\(=\left(4x^2-4x+1\right)-\left(y^2+8y+16\right)\)
\(=\left(2x-1\right)^2-\left(y+4\right)^2\)
\(=\left(2x-1-y-4\right)\left(2x-1+y+4\right)\)
\(=\left(2x-y-5\right)\left(2x+y+3\right)\)
5: \(\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y\right)^2-2\left(x+y\right)\cdot1+1^2\)
\(=\left(x+y-1\right)^2\)
7: \(\left(x+y\right)^2-8\left(x+y\right)+12\)
\(=\left(x+y\right)^2-2\left(x+y\right)-6\left(x+y\right)+12\)
\(=\left(x+y\right)\left(x+y-2\right)-6\left(x+y-2\right)\)
=(x+y-2)(x+y-6)
9: \(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)=\left(x^2+x+6\right)\left(x+2\right)\left(x-1\right)\)
11: \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)^2-5\left(x^2+x\right)+3\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)\left(x^2+x-5\right)+3\left(x^2+x-5\right)\)
\(=\left(x^2+x-5\right)\left(x^2+x+3\right)\)
