Example 38

$\;\;\;(7u^{5} + 3v^{8})^2$

$=(A + B)^2 \text{, where } A = 7u^{5} \text{ and } B = 3v^{8} $

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

$=(7u^{5})^2 + 2(7u^{5})(3v^{8}) + (3v^{8})^2 $

$=49u^{10} + 42u^{5}v^{8} +9v^{16} $