When \(|x|<1/2\), the coefficient of \(x^6\) in the expansion of \((\frac{2-x^2}{1+2x})^6\) is
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When finding a coefficient in the product of two expansions, systematically list the pairs of terms whose powers add up to the desired power. For \((a_0+a_1x+...)(b_0+b_1x+...)\), the coefficient of \(x^n\) is \(a_0b_n + a_1b_{n-1} + a_2b_{n-2} + \dots + a_nb_0\).