Q. 61 - Intermediate Algebra

Question

In the following exercises, add or subtract the polynomials. 

$\left(x^3-x^{2}y\right)-\left(4x{y}^2-y^3\right)+\left(3x^{2}y-x{y}^2\right)$

Step-by-Step Solution

Answer

Hence,

$\left(x^3-x^{2}y\right)-\left(4x{y}^2-y^3\right)+\left(3x^{2}y-x{y}^2\right)=x^3+2x^{2}y-5x{y}^2+y^3$

Step 1. Given information

$\begin{array}{l}\text{The given expressions is}\\ \left(x^3-x^{2}y\right)-\left(4x{y}^2-y^3\right)+\left(3x^{2}y-x{y}^2\right)\\ \text{We have to add or subtract the polynomials as applicable.}\end{array}$

Step 2. Simplify

$\begin{array}{l}\Rightarrow \left(x^3-x^{2}y\right)-\left(4x{y}^2-y^3\right)+\left(3x^{2}y-x{y}^2\right)\\ =x^3-x^{2}y-4x{y}^2+y^3+3x^{2}y-x{y}^2\left[\text{Rewrite without parentheses}\right]\\ =x^3-x^{2}y+3x^{2}y-4x{y}^2-x{y}^2+y^3\left[\text{Combine the like terms}\right]\\ =x^3+2x^{2}y-5x{y}^2+y^3\left[\text{Simplify}\right]\end{array}$