Question

Subtract polynomials ( x^3 - 2x^2y) - ( xy^2 - 3y^3) - ( x^2y - 4xy^2)

Answer 1

We are given the following operation of polynomials:

`\mleft(x^3-2x^2y\mright)-(xy^2-3y^3)-(x^2y-4xy^2)`

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:

`x^3-2x^2y-xy^2+3y^3-x^2y+4xy^2`

Now, we associate like terms. This means the terms that have the same variables elevated at the same exponents, like this:

`(x^3)+(-2x^2y-x^2y)+(-xy^2+4xy^2)+(3y^3)`

Now, we add the coefficients of the like terms:

`x^3-3x^2y+3xy^2+3y^3`

Since we can't simplify any further this is the final answer.