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Why: $7+2\cdot(11\cdot 2^{k-1} - 7) $= Left side
equals $11\cdot 2^k -7$ = right side.So, what I'm asking here is, what operations are used on left side to achieve right side?

$7+2\cdot (11\cdot 2^{k-1} - 7) = 11\cdot 2^k -7$

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well, the usual operations^^ – awllower Apr 8 '11 at 14:29
up vote 2 down vote accepted

Use the distributive and commutative properties: $A \cdot (B-C) = A \cdot B - A\cdot C$. One point to note is that $2 \cdot 2^{k-1} = 2^k$.

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