We are given the following operation of polynomials:
[tex]\mleft(x^3-2x^2y\mright)-(xy^2-3y^3)-(x^2y-4xy^2)[/tex]First, we will apply the distributive property on the parenthesis. This means that we will change the sign of the terms inside each of the parenthesis that have a minus sign on the left side, like this:
[tex]x^3-2x^2y-xy^2+3y^3-x^2y+4xy^2[/tex]Now, we associate like terms. This means the terms that have the same variables elevated at the same exponents, like this:
[tex](x^3)+(-2x^2y-x^2y)+(-xy^2+4xy^2)+(3y^3)[/tex]Now, we add the coefficients of the like terms:
[tex]x^3-3x^2y+3xy^2+3y^3[/tex]Since we can't simplify any further this is the final answer.
