Expansions!

Discrete Mathematics Level pending

The expression\[(2a^2 + 3b)^9 - k(3a + 2b)^{12}\]where \(k\) is a real number, has 21 terms in its expansion. If the value of \(k\) (in simplest form) is of the form \(\frac{a}{b}\), where \(a\) and \(b\) are positive integers, find the value of \(a+b\).

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