Chapter 4.2, Problem 34E

To determine

To find: the total cost of books by using the polynomial identity $\left(a+b\right)\left(a-b\right)=a^2-b^2$ and mental math.

Answer to Problem 34E

Total cost of the book is $\$899$ .

Explanation of Solution

Given information:

Number of books is 29 and cost of each book is $31.

Calculation:

Cost of each book is $31.

Number of books is 29.

So, the total cost of book can be found by the polynomial identity $\left(a+b\right)\left(a-b\right)=a^2-b^2$ .

  $\begin{array}{c}\$31\times 29=\left(30+1\right)\left(30-1\right)\\ ={30}^2-1^2\\ =900-1\\ =\$899\end{array}$

Therefore, total cost of the book is $\$899$ .

Now, the total cost can be found by the product

  $\$31\times 29=\$899$

Hence, the result is verified.