Example 62

$\;\;\;(4a - 9b^{2})^2$

$=(A - B)^2 \text{, where } A = 4a \text{ and } B = 9b^{2} $

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

$=(4a)^2 - 2(4a)(9b^{2}) + (9b^{2})^2 $

$=16a^{2} - 72ab^{2} +81b^{4} $