Chapter 14.4, Problem 19PPS

To determine

Tosimplify:the given equation.

Answer to Problem 19PPS

  $5t^2\left(t+2\right)-5t\left(4t^2-3t\right)=-15t^3+25t^2$

Explanation of Solution

Given:

The given equation: $5t^2\left(t+2\right)-5t\left(4t^2-3t\right)$

Calculation:

As thegiven equation is $5t^2\left(t+2\right)-5t\left(4t^2-3t\right)$ .

Simplify the equation by open the parenthesis, then

  $\begin{array}{l}5t^2\left(t+2\right)-5t\left(4t^2-3t\right)\\ =5t^2\left(t\right)+5t^2\left(2\right)-5t\left(4t^2\right)-5t\left(-3t\right)\{\text{open the parenthesis}}\\ =5t^3+10t^2-20t^3+15t^2\{\text{simplify}}\\ =-15t^3+25t^2\left\{combinetheliketerms\right\}\end{array}$

Hence, the value of the given simplification is $5t^2\left(t+2\right)-5t\left(4t^2-3t\right)=-15t^3+25t^2$ .