Distributive Property Misconception

$(a \cdot b)+c \neq +c (a \cdot b)$

Here's why:

One may argue that just by changing the position of $+c$ in the equation, they will be equal by Commutative Property of Addition , but by simplifying the result, each expression will yield a different answer.

$(a \cdot b)+c \overset{?}{=} +c (a \cdot b)$ $\color{#D61F06}{ab} \color{#333333}{+c} \overset{?}{=} \color{#D61F06}{a} \color{#333333}{c+} \color{#D61F06}{b} \color{#333333}{c}$

Hence,

$\color{#D61F06}{ab} \color{#333333}{+c} \neq \color{#D61F06}{a} \color{#333333}{c+} \color{#D61F06}{b} \color{#333333}{c}$

REMEMBER , addition does not distribute across multiplication in the left part of the equation.