Final answer:
To factor the difference of two cubes, use the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Step-by-step explanation:
To factor the difference of two cubes, we can use the formula (a^3 - b^3) = (a - b)(a^2 + ab + b^2), where a = 2x and b = 3y. Plugging in these values, we get:
24x^3 - 81y^3 = (2x - 3y)(4x^2 + 6xy + 9y^2)
Therefore, the difference of two cubes 24x^3 - 81y^3 can be factored completely into (2x - 3y)(4x^2 + 6xy + 9y^2).