Use the Binomial Theorem or Pascal's Triangle to expand the binomial.
(2x - 3y)^3
Using the Binomial Theorem, the expansion of (2x - 3y)^3 can be found by using the formula:
(2x - 3y)^3 = C(3,0)(2x)^3(-3y)^0 + C(3,1)(2x)^2(-3y)^1 + C(3,2)(2x)^1(-3y)^2 + C(3,3)(2x)^0(-3y)^3
Where C(n,r) represents the binomial coefficient "n choose r", which can be found using Pascal's Triangle.
Expanding and simplifying each term, we have:
= 1(2x)^3 + 3(2x)^2(-3y) + 3(2x)(-3y)^2 + 1(-3y)^3
= 8x^3 - 12x^2y + 18xy^2 - 27y^3
Therefore, (2x - 3y)^3 expands to 8x^3 - 12x^2y + 18xy^2 - 27y^3.