Question

1. explain what the following equation means in context of hot and cold cubes. 2(-3)-2(4)
2. explain what the following equation means in context of hot and cold cubes. -3(-4)+4(-3)

Explanation:

In the context of hot and cold cubes, positive numbers can represent hot cubes (adding heat) and negative numbers can represent cold cubes (removing heat). Multiplication represents combining a certain number of groups of cubes. For the expression 2(-3) - 2(4), 2(-3) means 2 groups of 3 cold - cubes (removing 6 units of heat in total from the initial state), and 2(4) means 2 groups of 4 hot - cubes (adding 8 units of heat in total). The subtraction between them represents the net change in heat considering these two operations. For - 3(-4)+4(-3), - 3(-4) means removing 3 groups of 4 cold - cubes (which is equivalent to adding 12 units of heat), and 4(-3) means 4 groups of 3 cold - cubes (removing 12 units of heat).

Answer:

The first expression 2(-3) - 2(4) represents a net change in heat where 6 units of heat are removed due to cold - cube groups and 8 units of heat are added due to hot - cube groups. The second expression - 3(-4)+4(-3) represents a situation where initially 12 units of heat are added by removing cold - cube groups and then 12 units of heat are removed by adding cold - cube groups.