Example 16

$\;\;\;(3u^{9} + 2v^{7})^2$

$=(A + B)^2 \text{, where } A = 3u^{9} \text{ and } B = 2v^{7} $

$=A^2 + 2AB + B^2$

$=(3u^{9})^2 + 2(3u^{9})(2v^{7}) + (2v^{7})^2 $

$=9u^{18} + 12u^{9}v^{7} +4v^{14} $