Write the following cube in expanded form:
$(3x + 2y)^3$

To expand $(3x + 2y)^3$,we use the algebraic identity: $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$.
Here,$a = 3x$ and $b = 2y$.
Substituting these values into the identity:
$(3x + 2y)^3 = (3x)^3 + (2y)^3 + 3(3x)(2y)(3x + 2y)$
$= 27x^3 + 8y^3 + 18xy(3x + 2y)$
$= 27x^3 + 8y^3 + 54x^2y + 36xy^2$