Chapter 4.3, Problem 2AGP

To determine

To calculate: The factors of the polynomial $20x^{2}y-15x{y}^2$ .

Answer to Problem 2AGP

The polynomial is factored as $5xy\left(4x-3y\right)$ .

Explanation of Solution

Given information:

The polynomial $20x^{2}y-15x{y}^2$ .

Formula used:

The greatest common factor GCF is denoted as $a^3{b}^2-na{b}^2=a{b}^2\left(a^2-n\right)$ .

Calculation:

Consider the polynomial $20x^{2}y-15x{y}^2$ .

Recall that greatest common factor GCF is denoted as $a^3{b}^2-na{b}^2=a{b}^2\left(a^2-n\right)$ .

Apply it, and then use the distributive property to combine the terms.

  $\begin{array}{c}20x^{2}y-15x{y}^2=5xy\left(4x\right)-5xy\left(3y\right)\\ =5xy\left(4x-3y\right)\end{array}$

Thus, the polynomial is factored as $5xy\left(4x-3y\right)$ .