Write the following cube in expanded form: $(2a - 3b)^{3}$

(N/A) To expand $(2a - 3b)^{3}$,we use the algebraic identity: $(x - y)^{3} = x^{3} - y^{3} - 3xy(x - y)$.
Here,$x = 2a$ and $y = 3b$.
Substituting these values into the identity:
$(2a - 3b)^{3} = (2a)^{3} - (3b)^{3} - 3(2a)(3b)(2a - 3b)$
Calculating the cubes and the product:
$= 8a^{3} - 27b^{3} - 18ab(2a - 3b)$
Distributing $-18ab$ inside the parentheses:
$= 8a^{3} - 27b^{3} - (36a^{2}b - 54ab^{2})$
$= 8a^{3} - 27b^{3} - 36a^{2}b + 54ab^{2}$