Chapter 8.7, Problem 47PPE

To determine

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

Answer to Problem 47PPE

The factors of 84 are 6 and 14, so $84=6\cdot 14$ .

Explanation of Solution

Given information:

The given number is 84.

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 84 that may be written as

  $84=100-16$

Difference of two numbers each square of some number

  $84={\left(10\right)}^2-{\left(4\right)}^2$

Difference of two squares

  $84=\left(10-4\right)\left(10+4\right)$$\because a^2-b^2=\left(a-b\right)\left(a+b\right)$

  $84=\left(6\right)\left(14\right)$ .

Thus, the factors of 84 are 6 and 14, so $84=6\cdot 14$ .

Conclusion:

The factors of 84 are 6 and 14, so $84=6\cdot 14$ .