Answer
$\sin^{2}\theta - 8 \sin\theta + 16 $
Work Step by Step
Given expression-
$(\sin\theta - 4)^{2}$
= $(\sin\theta - 4) (\sin\theta - 4)$
(Recall $a^{2} = a\times a$)
= $\sin\theta. \sin\theta - 4 \sin\theta - 4 \sin\theta + 16 $
(By FOIL method)
= $\sin^{2}\theta - 8 \sin\theta + 16 $
ALTERNATE METHOD
Recall $ (A-B)^{2} = A^{2} - 2 AB + B^{2}$
Therefore-
$(\sin\theta - 4)^{2} = \sin^{2}\theta - 2 \sin\theta .4 + 4^{2}$
= $\sin^{2}\theta - 8 \sin\theta + 16$
