Chapter 4, Problem 4CT

To determine

To Simplify:

To simplify $3x{y}^2\left(x^2-2xy\right)$ .

Answer to Problem 4CT

The simplified solution to $3x{y}^2\left(x^2-2xy\right)$ is $3x^3{y}^2-6x^2{y}^3$ .

Explanation of Solution

Given information:

The given equation is $3x{y}^2\left(x^2-2xy\right)$ .

Formula:

Distributive law: $a\left(b-c\right)=ab-ac$ .

Consider $3x{y}^2\left(x^2-2xy\right)$ ,

Apply the distributive law $a\left(b-c\right)=ab-ac$ ,

Here

  $\begin{array}{l}a=3x{y}^2\\ b=x^2\\ c=2xy\end{array}$

  $\begin{array}{l}\Rightarrow 3x{y}^2{x}^2-3x{y}^2\cdot 2xy\\ =3x^3{y}^2-6x^2{y}^3\end{array}$

Therefore, the simplified solution to $3x{y}^2\left(x^2-2xy\right)$ is $3x^3{y}^2-6x^2{y}^3$ .