Chapter 8.2, Problem 38PPS

To determine

To simplify: The expression $\frac{3}{5}{r}^{2}t\left(10r^3+5r{t}^3+15t^2\right)$

Answer to Problem 38PPS

  $6r^{5}t+3r^3{t}^4+9r^2{t}^3$

Explanation of Solution

Given:

  $\frac{3}{5}{r}^{2}t\left(10r^3+5r{t}^3+15t^2\right)$

Calculation:

The given expression is $\frac{3}{5}{r}^{2}t\left(10r^3+5r{t}^3+15t^2\right)$

Distribute $\frac{3}{5}{r}^{2}t$ over the parenthesis

  $\frac{3}{5}{r}^{2}t\cdot 10r^3+\frac{3}{5}{r}^{2}t\cdot 5r{t}^3+\frac{3}{5}{r}^{2}t\cdot 15t^2$

Simplify the expression

  $6r^{5}t+3r^3{t}^4+9r^2{t}^3$