Two sides of equation

Question

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?

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

Answer 1

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