Explanation

(b)
$\left( 1 + x^{2} \right)^{5}(1 + x)^{4}$
$= \left( \ ^{5}C_{0} + \ ^{5}C_{1}x^{2} + \ ^{5}C_{2}x^{4} + \ldots \right)(\ ^{4}C_{0} +^{4}C_{1}x$
+$\ ^{4}C_{2}x^{2} + \ ^{4}C_{3}x^{3} + \ ^{4}C_{4}x^{4}$
The coefficient of $x^{5}$ in $\left\lbrack {1 + x}^{2})^{5}(1 + x)^{4} \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ ^{5}C_{2} \bullet \ ^{4}C_{1} + \ ^{5}C_{1} \bullet \ ^{4}C_{3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 10 \bullet 4 + 4 \bullet 5 = 60$