Example 12

$\;\;\;(u^{4} + 9v^{10})^2$

$=(A + B)^2 \text{, where } A = u^{4} \text{ and } B = 9v^{10} $

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

$=(u^{4})^2 + 2(u^{4})(9v^{10}) + (9v^{10})^2 $

$=u^{8} + 18u^{4}v^{10} +81v^{20} $