Chapter 8.7, Problem 46PPE

To determine

To find: A pair of factors for the given number 224 by using the difference of two squares.

Answer to Problem 46PPE

The factors of 224 are 14 and 16, so $224=14\cdot 16$ .

Explanation of Solution

Given information:

The given number is 224.

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 224 that may be written as

  $224=225-1$

  $224={\left(15\right)}^2-{\left(1\right)}^2$

Difference of two squares

  $224=\left(15-1\right)\left(15+1\right)$$\because a^2-b^2=\left(a-b\right)\left(a+b\right)$

  $224=\left(14\right)\left(16\right)$ .

Thus, the factors of 224 are 14 and 16, so $224=14\cdot 16$ .

Conclusion:

The factors of 224 are 14 and 16, so $224=14\cdot 16$ .