The discussion revolves around evaluating the expression $2\left(24^3-3*24^2*4+3*24*4^2-4^3\right)$ using the expansion of $(x-y)^3$. Participants explore the relationship between the expression and the binomial expansion.
Participants generally agree on the simplification of the expression to $2(24 - 4)^3$, but there is no explicit consensus on the overall evaluation process or the initial approach to the problem.
There are no stated limitations or unresolved mathematical steps, but the discussion reflects varying levels of clarity on the evaluation process.
Readers interested in mathematical expansions, binomial theorem applications, or those seeking problem-solving strategies in algebra may find this discussion relevant.
The expansion is: \; (x-y)^3 \;=\;x^3 - 3\!\cdot\! x^2\!\cdot\! y + 3\!\cdot \!x\!\cdot\! y^2 - y^3mathlearn 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: \; (x-y)^3 \;=\;x^3 - 3\!\cdot\! x^2\!\cdot\! y + 3\!\cdot \!x\!\cdot\! y^2 - y^3
. . . . . . . . . Compare that to: 24^3 - 3\!\cdot\! 24^2\!\cdot\! 4 + 3\!\cdot\! 24\!\cdot\! 4^2 - 4^3Can you see that it is equal to (24 - 4)^3 \;=\;20^3 \;=\;8,000
mathlearn said:$2\left(24^3-3*24^2*4+3*24*4^2-4^3\right)$