What is the binomial expansion of $(2x+1/x)^7$ ?

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Answer 1 · 2015-05-26T18:01:33

The 8th row of Pascal's triangle goes:

$1$ , $7$ , $21$ , $35$ , $35$ , $21$ , $7$ , $1$

Multiply this by descending powers of 2:

$128$ , $64$ , $32$ , $16$ , $8$ , $4$ , $2$ , $1$

To get the sequence:

$128$ , $448$ , $672$ , $560$ , $280$ , $84$ , $14$ , $1$

So:

$(2x+1/x)^7$

$=128x^7 + 448x^5 + 672x^3 + 560x + 280/x + 84/x^3 + 14/x^5 + 1/x^7$

What is the binomial expansion of (2x+1/x)^7 (2x+1/x)^7 ?