Example 13

$\;\;\;(4a^{2} + 3b^{4})^2$

$=(A + B)^2 \text{, where } A = 4a^{2} \text{ and } B = 3b^{4} $

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

$=(4a^{2})^2 + 2(4a^{2})(3b^{4}) + (3b^{4})^2 $

$=16a^{4} + 24a^{2}b^{4} +9b^{8} $