\(\begin{array}{l} a)\,\,2{x^2} - 12x + 18 + 2xy - 6y\\ = 2\left( {{x^2} - 6x + 9} \right) + 2y\left( {x - 3} \right)\\ = 2{\left( {x - 3} \right)^2} + 2y\left( {x - 3} \right)\\ = 2\left( {x - 3} \right)\left( {x - 3 + y} \right).\\ b)\,\,{x^2} + 4x - 4{y^2} + 8y\\ = \left( {{x^2} - 4{y^2}} \right) + \left( {4x + 8y} \right)\\ = \left( {x - 2y} \right)\left( {x + 2y} \right) + 4\left( {x + 2y} \right)\\ = \left( {x + 2y} \right)\left( {x - 2y + 4} \right). \end{array}\)
