Question 1178563
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DO NOT expand the second factor completely and then multiply the result by the first factor.  That is WAY too much work!<br>
The second factor, when expanded, will contain terms of x^12, x^7, x^2, x^-3, x^-8, x^-13, and x^-18.<br>
The only place where we will get a constant term (x^0) when that factor is multiplied by (1-x^2+x^3) is when the x^3 in the first factor is multiplied by the x^-3 term in the second factor.<br>
The coefficient of the x^-3 term in the expanded second factor is<br>
{{{C(6,3)(3^3)((-5/7)^3) = (20)(27)(-125/343) = -67500/343}}}<br>
Then the constant term in the completely expanded expression is<br>
{{{(1)(-67500/343) = -67500/343}}}<br>