\(1,=\left(x-2\right)\left(x+2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-1\right)\\ 2,=\left(x-5\right)\left(x+5\right)-y\left(x-5\right)=\left(x-5\right)\left(x-y+5\right)\\ 3,=x^3-2x^2+3x^2-6x+4x-8=\left(x-2\right)\left(x^2+3x+4\right)\\ 4,=x^3+2x^2-6x^2-12x+4x+8=\left(x+2\right)\left(x^2-6x+4\right)\\ 5,=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\\ 6,=\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)=\left(x-2y\right)\left(x+2y+2\right)\\ 7,=3\left(x-y\right)\left(x+y\right)+4\left(x-y\right)=\left(x-y\right)\left(3x+3y-4\right)\\ 8,=x^4+5x^3-3x^2+3x^2+15x-9\\ =x^2\left(x^2+5x-3\right)+3\left(x^2+5x-3\right)\\ =\left(x^2+3\right)\left(x^2+5x-3\right)\\ 9,=x^4-3x^3-3x^3+9x^2-9x^2+27x+27x-81\\ =\left(x-3\right)\left(x^3-3x^2-9x+27\right)\\ =\left(x-3\right)\left[x^2\left(x-3\right)-9\left(x-3\right)\right]\\ =\left(x-3\right)^3\left(x+3\right)\)
