a) \(x^2+y^2-z^2+2xy-2z-1\)
\(=\left(x^2+y^2+2xy\right)-\left(z^2+2z+1\right)\)
\(=\left(x+y\right)^2-\left(z+1\right)^2\)
\(=\left(x+y+z+1\right)\left(x+y-z-1\right)\)
b) \(\left(a+b+c\right)^2+\left(a-b+c\right)^2-4b^2\)
\(=\left(a+b+c\right)^2+\left(a-b+c-2b\right).\left(a-b+c+2b\right)\)
\(=\left(a+b+c\right)^2+\left(a-3b+c\right)\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a+b+c+a-3b+c\right)\)
\(=\left(a+b+c\right)\left(2a-2b+2c\right)\)
\(=2.\left(a+b+c\right)\left(a-b+c\right)\)