Chapter 8.7, Problem 44PPE

To determine

To find: A pair of factors for the given number 143 by using the difference of two squares.

Answer to Problem 44PPE

The factors of 143 are 11 and 13, so $143=11\cdot 13$ .

Explanation of Solution

Given information:

The given number is 143.

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 143 that may be written as

  $143=144-1$

  $143={\left(12\right)}^2-{\left(1\right)}^2$

Difference of two squares

  $143=\left(12-1\right)\left(12+1\right)$$\because a^2-b^2=\left(a-b\right)\left(a+b\right)$

  $143=\left(11\right)\left(13\right)$ .

Thus, the factors of 143 are 11 and 13, so $143=11\cdot 13$ .

Conclusion:

The factors of 143 are 11 and 13, so $143=11\cdot 13$ .