a) \(x^2+2x+1-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
b) \(25x^2+1-9y^2-10x\)
\(=25x^2-10x+1-9y^2\)
\(=\left(5x-1\right)^2-9y^2\)
\(=\left(5x-1+3y\right)\left(5x-1-3y\right)\)
c) \(x^2-1+4y-4y^2\)
\(=x^2-\left(1-4y+4y^2\right)\)
\(=x^2-\left(1-2y\right)^2\)
\(=\left(x+1-2y\right)\left(x-1+2y\right)\)