<PRE><B>Question 1170639</B>
&lt;br&gt;
The expansion of the second factor will be in the form&lt;br&gt;
{{{Ax^6+Bx^4+Cx^2+D+E/x^2+F/x^4+G/x^6}}}&lt;br&gt;
When that is multiplied by {{{2+2/x^2}}}, we will get constant partial products from two places: {{{(D)(2)}}} and {{{(Cx^2)(2/x^2)}}}&lt;br&gt;
So the constant term in the final expansion will be {{{2C+2D}}}&lt;br&gt;
So we need to calculate the coefficients of the constant and x^2 terms, C and D.&lt;br&gt;
{{{D = C(6,3)((1^3)((-3)^3)) = (20)(1)(-27) = -540}}}&lt;br&gt;
{{{C = C(6,4)((1^4)((-3)^2)) = (15)(1)(9) = 135}}}&lt;br&gt;
Then&lt;br&gt;
{{{2C+2D = 2(C+D) = 2(-540+135) = 2(-405) = -810}}}&lt;br&gt;
ANSWER: -810&lt;br&gt;
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