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1. convert polar equation to rectangular coordinates:

r^2=4sin2theta

2. find the coefficient of x^5 in the expansion (x+2)(x+1)^8

x^2 + y^2 = r^2
x = rcosθ
y = rsinθ

r^2 = 4 sin2θ
r^2 = 8sinθcosθ
r^2 = 8 * y/r * x/r
r^4 = 8xy
(x^2 + y^2)^2 - 8xy = 0

(x+1)^8 = x^8 + 8x^7 + 28x^6 + 56x^5 + 70x^4 + ...
(x+2)(x+1)^8 = ... + 70x^5 + ... + 112x^5 + ...
= ... + 182x^5 + ...

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