Example 20

$\;\;\;(5x^{4} + 11y^{4})^2$

$=(A + B)^2 \text{, where } A = 5x^{4} \text{ and } B = 11y^{4} $

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

$=(5x^{4})^2 + 2(5x^{4})(11y^{4}) + (11y^{4})^2 $

$=25x^{8} + 110x^{4}y^{4} +121y^{8} $