1) $(x -4)^2 + (x-4)$
$= (x- 4)(x -4 + 1)$
$= (x -4)(x -3)$
2a) $x^2 - 4x + 4 = 9(x -2)$
$\Leftrightarrow (x-2)^2 - 9(x -2)=0$
$\Leftrightarrow (x -2)(x -2-9)=0$
$\Leftrightarrow (x -2)(x -11) = 0$
$\Leftrightarrow \left[\begin{array}{l}x -2= 0\\x -11 = 0\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x = 2\\x =11\end{array}\right.$
b) $(x -1)^3 + 3(x+1)^2 = (x^2 - 2x + 4)(x+2)$
$\Leftrightarrow x^3 - 3x^2 + 3x -1 + 3(x^2 + 2x +1) = x^3 - 8$
$\Leftrightarrow 9x = - 10$
$\Leftrightarrow x = -\dfrac{10}{9}$
