Explanation

(d)
$\left( \sin^{2}\theta \right)^{3} + ({\cos^{2}{\theta)}}^{3} + 3\sin^{2}{\theta\cos^{2}\theta}$
$= \left( \sin^{2}{\theta + \cos^{2}\theta} \right)\left( \sin^{4}{\theta + \cos^{4}\theta} - \sin^{2}{\theta\cos^{2}\theta} \right) + 3\sin^{2}{\theta\cos^{2}\theta}$
$= 1\left\lbrack \left( \sin^{2}{\theta + \cos^{2}\theta} \right)^{2} - 3\sin^{2}{\theta\cos^{2}\theta} \right\rbrack + 3\sin^{2}{\theta\cos^{2}{\theta = 1}}$
$= 1 - 3\sin^{2}{\theta\cos^{2}{\theta + 3\sin^{2}{\theta\cos^{2}{\theta = 1}}}}$