Answer
a) $= (2x + 1)(x+1)$
b) $= (2sin\theta + 1)(sin\theta + 1)$
Work Step by Step
a) $2x^{2} +3x + 1$
$= 2x^{2} + 2x + 1x + 1$
$= 2x(x + 1) + 1(x+1)$
$= (2x + 1)(x+1)$.
b) $2(sin\theta)^{2} + 3sin\theta + 1$
Let $sin\theta = x$ to get
$2x^{2} + 3x + 1$ (Exact same equation as in Section a)
$= (2x+1)(x+1)$
Replace $x = sin\theta$ to get
$(2sin\theta + 1)(sin\theta + 1)$.