Chapter 4.3, Problem 34WE

To determine

To calculate: The multiplication of the term $\left(3s+2t\right)\left(s^3-3s{t}^2+2t^3\right)$ .

Answer to Problem 34WE

The required multiplication is $3s^4-9s^2{t}^2+2t{s}^3+4t^4$ .

Explanation of Solution

Given information:

The algebraic term is $\left(3s+2t\right)\left(s^3-3s{t}^2+2t^3\right)$ .

Formula Used:

Distribution property is

  $\begin{array}{c}\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)\\ =ac+ad+bc+bd\end{array}$

Calculation:

Consider the given algebraic term $\left(3s+2t\right)\left(s^3-3s{t}^2+2t^3\right)$ .

Now multiply. Use the distribution property.

  $\begin{array}{c}\left(3s+2t\right)\left(s^3-3s{t}^2+2t^3\right)=3s\left(s^3-3s{t}^2+2t^3\right)+2t\left(s^3-3s{t}^2+2t^3\right)\\ =3s^4-9s^2{t}^2+6s{t}^3+2t{s}^3-6s{t}^3+4t^4\\ =3s^4-9s^2{t}^2+2t{s}^3+4t^4\end{array}$

Hence, the required multiplication is $3s^4-9s^2{t}^2+2t{s}^3+4t^4$ .