mathlearn said:Considering the expansion of $(x-y)^3$ , Find the value of $2\left(24^3-3*24^2*4+3*24*4^2-4^3\right)$
Any Ideas on how to begin ?
soroban said:
The expansion is: [tex]\; (x-y)^3 \;=\;x^3 - 3\!\cdot\! x^2\!\cdot\! y + 3\!\cdot \!x\!\cdot\! y^2 - y^3[/tex]
. . . . . . . . . Compare that to: [tex]24^3 - 3\!\cdot\! 24^2\!\cdot\! 4 + 3\!\cdot\! 24\!\cdot\! 4^2 - 4^3[/tex]Can you see that it is equal to [tex](24 - 4)^3 \;=\;20^3 \;=\;8,000[/tex]
mathlearn said:$2\left(24^3-3*24^2*4+3*24*4^2-4^3\right)$
Expansion refers to the increase in size, volume, or scope of something. In scientific terms, it can also refer to the expansion of the universe. It is important to consider expansion because it can impact various systems and processes, and understanding it can help with predicting and analyzing future changes.
The expansion of the universe is measured through the use of various methods, including the redshift of galaxies, the cosmic microwave background radiation, and the brightness of supernovae. These measurements help scientists determine the rate of expansion and how it has changed over time.
The expansion constant, also known as the Hubble constant, is a numerical value that represents the rate of expansion of the universe. It is currently estimated to be around 70 kilometers per second per megaparsec. This value is calculated using data from various observations and measurements, such as those mentioned in the previous question.
The expansion of the universe plays a significant role in the formation of galaxies and other celestial bodies. As the universe expands, it causes matter and energy to become more spread out, creating the conditions for the formation of structures like galaxies and galaxy clusters. It also affects the gravitational pull between objects, which can influence their movements and interactions.
Currently, there is no evidence to suggest that the expansion of the universe can be reversed or stopped. In fact, observations have shown that the expansion is accelerating, meaning it is getting faster over time. However, there are theories such as the Big Crunch that suggest the universe may eventually collapse in on itself, potentially reversing the expansion. Further research and observations are needed to fully understand the fate of the universe.