Final answer:
The difference of cubes, denoted as a³-b³, is factored into (a-b)(a²+ab+b²). This factoring method is significant in mathematics and has practical implications in geometry and science, influencing concepts like the surface area to volume ratio in cells.
Step-by-step explanation:
The a³-b³ formula represents the difference of cubes, which is a special factorization formula. It can be factored into (a-b)(a²+ab+b²).
To solve for a simple cubic difference, for example, 8 - 1, you would recognize that 8 is 2³ and 1 is 1³, which gives you (2-1)((2)²+(2)(1)+(1)²) resulting in (1)(4+2+1) which simplifies to 7.
This relationship between the volume of a cube and its sides shows how important cubing of exponentials is in geometry and various applications in the sciences, as the surface area to volume ratio has implications for cells and other structures.