Example 24

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

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

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

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

$=25v^{10} + 20uv^{5} +4u^{2} $