MHB Considering the expansion , Find the value

[mathlearn]

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 ? (Mmm)

 

[Greg]

$(x-y)^3=x^3-3x^2y+3xy^2-y^3$

 

[soroban]

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 ?

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]

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

Thank you (Yes) ,

As the problem states,

$2\left(24^3-3*24^2*4+3*24*4^2-4^3\right)$

It should be $2(24 - 4)^3 $, Agree ? (Nod)

 

[Greg]

Yes, which equals 16000.