a: \(16-x^2=4^2-x^2=\left(4-x\right)\left(4+x\right)\)
b: \(x^2-8x+16\)
\(=x^2-2\cdot x\cdot4+4^2\)
\(=\left(x-4\right)^2\)
c: \(x^2-2x+1-y^2\)
\(=\left(x^2-2x+1\right)-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1-y\right)\left(x-1+y\right)\)
d: \(x^2+2xy+y^2-1\)
\(=\left(x^2+2xy+y^2\right)-1\)
\(=\left(x+y\right)^2-1\)
\(=\left(x+y+1\right)\left(x+y-1\right)\)