Chapter 4, Problem 5CR

To determine

To Simplify:

To simplify $\left(3t-4\right)\left(2t+3\right)$ .

Answer to Problem 5CR

The simplified solution to $\left(3t-4\right)\left(2t+3\right)$ is option (a) $6t^2+t-12$ .

Explanation of Solution

Given information:

The given equation is $\left(3t-4\right)\left(2t+3\right)$ .

Formula:

Foil method: $\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$ .

Consider $\left(3t-4\right)\left(2t+3\right)$ ,

Apply the foil method $\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$ ,

Here

  $\begin{array}{l}a=3t\\ b=-4\\ c=2t\\ d=3\end{array}$

  $\begin{array}{l}\Rightarrow 3t\cdot 2t+3t\cdot 3+\left(-4\right)\cdot 2t+\left(-4\right)\cdot 3\\ =3\cdot 2tt+3\cdot 3t-4\cdot 2t-4\cdot 3\\ =6t^2+t-12\end{array}$

Therefore, the simplified solution to $\left(3t-4\right)\left(2t+3\right)$ is option (a) $6t^2+t-12$ .