Question

Calculate the following differences:
a. 30² - 29²
b. 41² - 40²
c. 18² - 17²

Answer 1

The differences between squares of consecutive numbers can be found using the formula (x+1)² - x² = 2x + 1. The differences calculated for the given numbers are: 59 for 30² - 29², 81 for 41² - 40², and 35 for 18² - 17².

Step-by-step explanation:

Calculating the Differences

To calculate the differences between squares of consecutive numbers, you can use the identity (x+1)² - x² = 2x + 1. Using this identity, let's solve each part:

1. 30² - 29²: Here, x = 29, so the difference is 2(29) + 1, which equals 59.
2. 41² - 40²: Here, x = 40, so the difference is 2(40) + 1, which equals 81.
3. 18² - 17²: Here, x = 17, so the difference is 2(17) + 1, which equals 35.

This method provides a quick way to calculate the differences without the need for laborious multiplication.