Question: How to restrict the domain of a variable when finding the Gcd of two polynomials?

Consider two polynomials p and q in t. For example, p(t)=t^2+2*t and q(t)=t^3*(t+2). I want to find Gcd(p,q). But before I find it, solve an inequality and obtain that t<>-2. After that when I evaluate Gcd(p,q), I dont want maple to return t*(t+2) as Gcd because t<>-2 and thus the factor (t+2) is an unwanted common divisor. Is there a way to tell maple that "find the Gcd over a spesific domain". Because, otherwise maple needlessly spend time for finding the gcd. Any help would be appreciated.

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