(2m-3n)^3 = (2m-3n)(2m-3n)(2m-3n)Expanding this using the distributive property:= (2m-3n)(4m^2-6mn-6mn+9n^2)= (2m-3n)(4m^2-12mn+9n^2)= 8m^3 -24m^2n + 18mn^2 - 12m^2n + 36mn^2 - 27n^3= 8m^3 - 36m^2n + 54mn^2 - 27n^3
Therefore, (2m-3n)^3 = 8m^3 - 36m^2n + 54mn^2 - 27n^3.
(2m-3n)^3 = (2m-3n)(2m-3n)(2m-3n)
Expanding this using the distributive property:
= (2m-3n)(4m^2-6mn-6mn+9n^2)
= (2m-3n)(4m^2-12mn+9n^2)
= 8m^3 -24m^2n + 18mn^2 - 12m^2n + 36mn^2 - 27n^3
= 8m^3 - 36m^2n + 54mn^2 - 27n^3
Therefore, (2m-3n)^3 = 8m^3 - 36m^2n + 54mn^2 - 27n^3.