How do you expand $(z+1/z)^2$ ?

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Answer 1 · 2016-11-14T07:26:05

$=z^2 +2 + 1/z^2$

Do not be put off by the fraction.

$(z +1/z)^2 = (z+1/z)(z+1/z)$

Multiply the 2 brackets - the FOIL method if you use it.

$(color(blue)(z)+color(red)(1/z))(z+1/z)$

$=color(blue)(z^2 +1) + color(red)(1+1/z^2)" "rarr cancelz/1 xx 1/cancelz = 1$

$=z^2 +2 + 1/z^2$

How do you expand (z+1/z)^2(z+1/z)^2?