x mũ 2-3x mũ 2-4x +12=? 9x mũ hai-36=? x mũ ba -x+3x mũ 2 y+3xy mũ hai+y mũ ba -y ax mũ hai+ay-bx mũ hai-by

\[\begin{array}{l} {x^2} - 3{x^2} - 4x + 12 = - 2{x^2} - 4x + 12\\ = - 2\left( {{x^2} + 2x - 6} \right) = - 2\left[ {\left( {{x^2} + 2x + 1} \right) - 7} \right]\\ = - 2\left[ {{{\left( {x + 1} \right)}^2} - 7} \right] = - 2\left( {x + 1 - \sqrt 7 } \right)\left( {x + 1 + \sqrt 7 } \right).\\ 9{x^2} - 36 = \left( {3x - 6} \right)\left( {3x + 6} \right).\\ {x^3} - x + 3{x^2}y + 3x{y^2} + {y^3} - y\\ = \left( {{x^3} + 3{x^2}y + 3x{y^2} + {y^3}} \right) - \left( {x + y} \right)\\ = {\left( {x + y} \right)^3} - \left( {x + y} \right)\\ = \left( {x + y} \right)\left[ {{{\left( {x + y} \right)}^2} - 1} \right]\\ = \left( {x + y} \right)\left( {x + y - 1} \right)\left( {x + y + 1} \right)\\ a{x^2} + ay - b{x^2} - by\\ = {x^2}\left( {a - b} \right) + y\left( {a - b} \right)\\ = \left( {a - b} \right)\left( {{x^2} + y} \right). \end{array}\]