Phân tích các đa thức sau thành nhân tử : a) x2 - 2x - 4y2 - 4y ; b) x4 + 2x3 - 4x - 4 ;

\[\begin{array}{l} a)\,\,{x^2} - 2x - 4{y^2} - 4y\\ = \left( {{x^2} - 4{y^2}} \right) - 2\left( {x + 2y} \right)\\ = \left( {x - 2y} \right)\left( {x + 2y} \right) - 2\left( {x + 2y} \right)\\ = \left( {x + 2y} \right)\left( {x - 2y - 2} \right).\\ b)\,\,\,{x^4} + 2{x^3} - 4x - 4\\ = {x^4} - 4 + \left( {2{x^3} - 4x} \right)\\ = \left( {{x^2} - 2} \right)\left( {{x^2} + 2} \right) + 2x\left( {{x^2} - 2} \right)\\ = \left( {{x^2} - 2} \right)\left( {{x^2} + 2x + 2} \right). \end{array}\]

a) \(x^2-2x-4y^2-4y\)

\(=(x^2-4y^2)-2(x+2y)\)

\(=(x+2y)(x-2y)-2(x+2y)\)

\(=(x+2y)(x-2y-2)\).

b) \( x^4+2x^3-4x-4\)

\(=(x^4-4)+2x(x^2-2)\)

\(=(x^2-2)(x^2+2)+2x(x^2-2)\)

\(=(x^2-2)(x^2+2x+2)\).