\(x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\\ 25x^2+1-9y^2-10x=\left(5x-1\right)^2-9y^2=\left(5x-3y-1\right)\left(5x+3y-1\right)\\ x^2-1+4y-4y^2=x^2-\left(2y-1\right)^2=\left(x-2y+1\right)\left(x+2y-1\right)\\ 9x^2+15x+5y+6xy+y^2\\ =\left(9x^2+6xy+y^2\right)+5\left(3x+y\right)\\ =\left(3x+y\right)^2+5\left(3x+y\right)\\ =\left(3x+y\right)\left(3x+y+5\right)\\ 9-x^2+6xy-9y^2=9-\left(x-3y\right)^2=\left(3-x+3y\right)\left(3+x-3y\right)\\ x^2+4x-2xy-4y+y^2\\ =\left(x^2-2xy+y^2\right)+\left(4x-4y\right)\\ =\left(x-y\right)^2+4\left(x-y\right)\\ =\left(x-y\right)\left(x-y+4\right)\\ 7y-4xy+14x-y^2-4x^2\\ =\left(-4x^2-4xy-y^2\right)+\left(7y+14x\right)\\ =7\left(2x+y\right)-\left(2x+y\right)^2\\ =\left(2x+y\right)\left(7-2x-y\right)\\ 3a-3b-a^2+2ab-b^2\\ =3\left(a-b\right)-\left(a-b\right)^2=\left(a-b\right)\left(3-a+b\right)\)
