[tex]\begin{gathered} (2x-3y)^3\text{ = }8x^3-36x^2y+54xy^2-27y^3 \\ \\ \text{option B} \end{gathered}[/tex]
In this question, we want to expand the given expression. We do this by multiplying the terms with itself three times
we have;
[tex]\begin{gathered} (2x-3y)^{3\text{ }}\text{ = (2x-3y)(2x-3y)(2x-3y)} \\ \\ =\text{ (2x(2x-3y) - 3y(2x-3y))}(2x-3y) \\ \\ =(4x^2-6xy-6xy+9y^2)(2x-3y) \\ \\ =(4x^2-12xy+9y^2)(2x-3y) \\ \\ =2x(4x^2-12xy+9y^2)-3y(4x^2-12xy+9y^2) \\ \\ =8x^3-24x^2y+18xy^2-12x^2y+36xy^2-27y^3 \\ \\ =8x^3-24x^2y-12x^2y+18xy^2+36xy^2-27y^3 \\ \\ =8x^3-36x^2y+54xy^2-27y^3 \end{gathered}[/tex]
