Chapter 6, Problem 2MCQ

To determine

To Evaluate: The simplified form of the expression $4t\left(3rt-r\right)$ where $r\ne 0,t\ne 0$ .

Answer to Problem 2MCQ

The value of the expression $4t\left(3rt-r\right)$ is $12t^{2}r-4tr$.

Explanation of Solution

Given information:

The expression is $4t\left(3rt-r\right)$ .

Formula used:

Distribution property states that multiplication of a term with sum or difference of two other terms same as add or subtract them separately after multiplication. That is

  $a\left(b\pm c\right)=ab\pm ac$

For any real value $x$ and integer $a$ , $b$ , product of power property states as $x^b\times x^a=x^{b+a}$ .

Calculation:

Consider the expression is $4t\left(3rt-r\right)$ .

Recall that distribution property states that multiplication of a term with sum or difference of two other terms same as add or subtract them separately after multiplication. That is

  $a\left(b\pm c\right)=ab\pm ac$

Apply it,

  $4t\left(3rt-r\right)=\left(4t\times 3rt\right)-\left(4t\times r\right)$

Again recall that for any real value $x$ and integer $a$ , $b$ , product of power property states as $x^b\times x^a=x^{b+a}$ .

Use it,

  $\begin{array}{c}\left(4t\times 3rt\right)-\left(4t\times r\right)=\left(12t^{1+1}r\right)-\left(4t\times r\right)\\ =12t^{2}r-4tr\end{array}$

Thus, the value of the expression $4t\left(3rt-r\right)$ is $12t^{2}r-4tr$ .