Chapter 4.6, Problem 8OE

To determine

To find: The increasing degree in the variable $x$ for expression $x{y}^2-3x^{2}y+2x^{3}y-2y$ .

Answer to Problem 8OE

The increasing degree in the variable $x$ for expression $x{y}^2-3x^{2}y+2x^{3}y-2y$ is $-2y+x{y}^2-3x^{2}y+2x^{3}y$ .

Explanation of Solution

Given:

The expression is $x{y}^2-3x^{2}y+2x^{3}y-2y$ .

Calculation:

The increasing degree in the variable $x$ for expression $x{y}^2-3x^{2}y+2x^{3}y-2y$ is calculated as follows:

  $\begin{array}{c}\text{Degree of }x\text{ in }x{y}^2=1\\ \text{Degree of }x\text{ in}-3x^{2}y=2\\ \text{Degree of }x\text{ in }2x^{3}y=3\\ \text{Degree of }x\text{ in }2y=0\end{array}$

Arrange in the increasing degree as follows:

  $-2y+x{y}^2-3x^{2}y+2x^{3}y$

Thus, the increasing degree in the variable $x$ for expression $x{y}^2-3x^{2}y+2x^{3}y-2y$ is $-2y+x{y}^2-3x^{2}y+2x^{3}y$ .