Write the following cubes in the expanded form: $(5 p-3 q)^{3}$

(N/A) To expand $(5 p-3 q)^{3}$,we use the algebraic identity: $(x-y)^{3} = x^{3} - y^{3} - 3xy(x-y)$.
Comparing $(5 p-3 q)^{3}$ with $(x-y)^{3}$,we identify $x = 5p$ and $y = 3q$.
Substituting these values into the identity:
$(5 p-3 q)^{3} = (5 p)^{3} - (3 q)^{3} - 3(5 p)(3 q)(5 p-3 q)$
Calculating the cubes and the product:
$= 125 p^{3} - 27 q^{3} - 45 pq(5 p-3 q)$
Distributing $-45 pq$ into the parentheses:
$= 125 p^{3} - 27 q^{3} - 225 p^{2} q + 135 p q^{2}$