\(4x^2+4x-9y^2+1\\ =\left(4x^2+4x+1\right)-9y^2\\ =\left(2x+1\right)^2-9y^2\\ =\left(2x+1\right)^2-\left(3y\right)^2\\ =\left[\left(2x+1\right)+3y\right]\left[\left(2x+1\right)-3y\right]\\ =\left(2x+1+3y\right)\left(2x+1-3y\right)\)
\(x^2-6xy+9y^2-25z^2\\ =\left(x^2-6xy+9y^2\right)-25z^2\\ =\left(x-3y\right)^2-25z^2\\ =\left(x-3y\right)^2-\left(5z\right)^2\\ =\left[\left(x-3y\right)+5z\right]\left[\left(x-3y\right)-5z\right]\\ =\left(x-3y+5z\right)\left(x-3y-5z\right)\)
\(x^2-xy+x-y\\ =\left(x^2-xy\right)+\left(x-y\right)\\ =x\left(x-y\right)+\left(x-y\right)\\ =\left(x-y\right)\left(x-1\right)\)
