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These should be very easy questions, but I really don't know how to get them right!

$1. \:$ Balance the equation $\sin(3t+2) = a\cos(3t) + b\sin(3t)$, get the value for $a$ and $b$.

$2. \:$ Balance the equation $e^{3y} = ae^y + be^{2y}$, also get the value for $a$ and $b$.

$3. \:$ Balance the equation $(x+2)^2 = a + bx + cx^2$, get value for $a$, $b$ and $c$.

Like question $3$, in common sense the answer should be $a = 4$, $b = 4$, $c = 1$. But I have no idea how I got wrong. Or maybe the balancing forcing terms require a different approach. Thanks in advance.

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    You can't balance equation $(2)$ whereas for equation $(1)$, $$\sin (3t+2)=\sin 2 \cos 3t+\cos 2 \sin 3t$$ – 2017-01-27
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    @NgChungTak How about the third one, why my solution is not correct? – 2017-01-27
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    Eq. $(3)$ is OK. – 2017-01-27

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