Example 40

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

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

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

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

$=49u^{4} + 126u^{2}v +81v^{2} $