Chapter 8.7, Problem 48PPE

To determine

To find: A pair of factors for the given number 84 by using the difference of two squares.

Answer to Problem 48PPE

The factors of 91are 7 and 13, so $91=7\cdot 13$ .

Explanation of Solution

Given information:

The given number is 91.

Formula used:

The factors of the difference of squares of two numbers a and b are: $a^2-b^2=\left(a-b\right)\left(a+b\right)$ .

Calculations:

The given number is 91 that may be written as

  $91=100-9$

Difference of two numbers each square of some number

  $91={\left(10\right)}^2-{\left(3\right)}^2$

Difference of two squares

  $91=\left(10-3\right)\left(10+3\right)$$\because a^2-b^2=\left(a-b\right)\left(a+b\right)$

  $91=\left(7\right)\left(13\right)$ .

Thus, the factors of 91are 7 and 13, so

  $91=7\cdot 13$ .

Conclusion:

The factors of 91are 7 and 13, so $91=7\cdot 13$ .