a. $(x+6)^2$
$=x^2+2.x.6+6^2$
$=x^2+12x+36$
b. $(2x-3)^2$
$=(2x)^2-2.2x.3+3^2$
$=4x^2-12x+9$
c. $(x+7)^3$
$=x^3+3.x^2.7+3.x.7^2+7^3$
$=x^3+21x^2+147x+343$
d. $\bigg(\dfrac{1}{3}x^2y-d\bigg)^3$
$=\bigg(\dfrac{1}{3}x^2y\bigg)^3-3.\bigg(\dfrac{1}{3}x^2y\bigg)^2.d+3.\dfrac{1}{3}x^2y.d^2-d^3$
$=\dfrac{1}{27}x^6y^3-\dfrac{1}{3}x^4y^2d+x^2yd^2-d^3$