a) \(1-2y+y^2\)
\(=y^2-2y+1\)
\(=\left(y-1\right)^2\)
b) \(\left(x+1\right)^2-25\)
\(=\left(x+1\right)^2-5^2\)
\(=\left(x+1-5\right)\left(x+1+5\right)\)
\(=\left(x-4\right)\left(x+6\right)\)
c) \(1-4x^2\)
\(=1^2-\left(2x\right)^2\)
\(=\left(1-2x\right)\left(1+2x\right)\)
d) \(8-27x^3\)
\(=2^3-\left(3x\right)^3\)
\(=\left(2-3x\right)\left(4+6x+9x^2\right)\)