E-PR03 · Negative powers contribute twice
Let \(\displaystyle P(x)=(x+\frac2x)^6(1+x^2)^2\), where \(x\ne0\).
Write the general term of the first factor.
Find the constant term of P, showing every contribution.
Find the coefficient of \(x^2\) in P. Explain why keeping only nonnegative powers of the first factor would fail.
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