Chapter 1.2, Problem 3P

To determine

To find: the value of the expression if $a=3\text{ and }b=4$ in two parts.

Answer to Problem 3P

  $\text{part}\left(a\right)-\text{part}\left(b\right)=-8.$

Explanation of Solution

Given:

  $\begin{array}{l}a=3\text{ and }b=4.\\ \left(a\right)3b-a^2.\\ \left(b\right)2b^2-7a.\end{array}$

Concept used:

In general, an expression is in simplest form when it is easiest to use.

Common ways to help it simplify is:

Combining like terms.

Factoring.

Expanding the opposite of factoring.

Clear out fractions by multiplying.

Recognizing the pattern and it has seen before, like the difference of squares etc.

Use bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ .

The variables can be put inside the equation and solved the equation.

Calculation:

According to the given expression:

  $\begin{array}{l}a=3\text{ and }b=4.\\ \left(a\right)3b-a^2.\\ \left(b\right)2b^2-7a.\end{array}$

By putting the value $a=3\text{ and }b=4$ in part $\left(a\right)\text{ and }\left(b\right)$ :

  $\begin{array}{l}\left(a\right)3b-a^2.\\ \Rightarrow 3\left(4\right)-3^2.\\ \Rightarrow 12-9=3.\end{array}$

Similarly, by putting the value $a=3\text{ and }b=4$ in part $\left(b\right)$ :

  $\begin{array}{l}\left(b\right)2b^2-7a.\\ \Rightarrow 2{\left(4\right)}^2-7\left(3\right).\\ \Rightarrow 32-21=11.\end{array}$

So, by taking the difference of part $a\text{ and }b$ as:

  $\begin{array}{l}\text{part}\left(a\right)-\text{part}\left(b\right).\\ \Rightarrow 3b^2-a^2-2b^2+7a.\\ \Rightarrow 3-11.\\ \Rightarrow -8.\end{array}$

Hence, $\text{part}\left(a\right)-\text{part}\left(b\right)=-8.$