Explanation

(a)
${(1 + x + x}^{2})^{- 3} = \left\lbrack \frac{1}{{(1 + x + x}^{2})} \right\rbrack^{3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack \frac{1 - x}{1 - x^{3}} \right\rbrack^{3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = (1 - x)^{3}({1 - x}^{3})^{- 3}$
$\ \ \ \ = \left( 1 - x^{3} - {3x}^{2} + 3x \right)\left( 1 + {3x}^{3} + {6x}^{6} + \ldots \right)$
$\therefore$ Coefficient of $x^{6}$ in ${(1 + x + x}^{2})^{- 3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 6 - 3 = 3$