Final answer:
The sum of cubes is the expression a³ + b³, and it can be represented by the formula (a + b)(a - ab + b²). Cubing exponentials involve raising the base to the third power and multiplying the exponential term's exponent by 3.
Step-by-step explanation:
Sum of Cubes Formula
The sum of cubes refers to the expression a³ + b³. To understand this expression, we can use the binomial theorem to expand (a + b)³, which gives us a³ + 3a²b + 3ab² + b³.
However, if we are specifically looking for a³ + b³, we can consider it as a special case where the middle terms cancel, which is represented by the formula a³ + b³ = (a + b)(a - ab + b²).
In the context of cubing of exponentials, when a number with an exponential term is cubed, the digit term is cubed in the usual way, and the exponent on the exponential term is multiplied by 3.
For example, if we have (2x)³, it would become 8x³, because 2 is cubed to get 8, and x's exponent 1 is multiplied by 3 to become x³.
Additionally, knowledge of how volume changes with physical conditions involves understanding that the volume (V) of a cube with changes in temperature can be approximated by using linear expansion coefficients. However, this is a separate application not directly tied to algebraic sums of cubes.