Example 39

$\;\;\;(u^{5} + 3v^{4})^2$

$=(A + B)^2 \text{, where } A = u^{5} \text{ and } B = 3v^{4} $

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

$=(u^{5})^2 + 2(u^{5})(3v^{4}) + (3v^{4})^2 $

$=u^{10} + 6u^{5}v^{4} +9v^{8} $