Enter a set of data to quickly calculate both the difference of squares and the square of the difference.
he difference of squares refers to the result of subtracting the squares of each number in a data set. For a data set \( x_1, x_2, \dots, x_n \), the formula for the difference of squares is: \( \text{Difference of Squares} = x_1^2 - x_2^2 - x_3^2 - \dots - x_n^2 \) In simple terms, you square each number and then perform the subtraction.
The square of the difference refers to first calculating the difference between all the numbers and then squaring that difference. The formula is: \( \text{Square of the Difference} = (x_1 - x_2 - x_3 - \dots - x_n)^2 \) The square of the difference is used to measure the deviation between data points, with the result being positive, even if the difference itself is negative.
The calculator supports custom delimiters and can process common delimiters such as commas, spaces, line breaks, semicolons, etc. By default, these are not required to be entered. However, if you use a special delimiter, like "|" or any other symbol, you can manually input the custom delimiter. It's important to ensure that thousand separators and number delimiters don't conflict. For example, a comma can be used for the thousand separator, but for number delimiters, you can choose other symbols like a space or semicolon.
Solution:
1. Difference of Squares:
\( \text{Difference of Squares} = 8^2 - 3^2 - 5^2 = 64 - 9 - 25 = 30 \)
Result: Difference of Squares = 30
2. Square of the Difference:
\( \text{Square of the Difference} = (8 - 3 - 5)^2 = 0^2 = 0 \)
Result: Square of the Difference = 0
Solution:
1. Difference of Squares:
\( \text{Difference of Squares} = 10^2 - 7^2 - 4^2 = 100 - 49 - 16 = 35 \)
Result: Difference of Squares = 35
2. Square of the Difference:
\( \text{Square of the Difference} = (10 - 7 - 4)^2 = (-1)^2 = 1 \)
Result: Square of the Difference = 1
Solution:
1. Difference of Squares:
\( \text{Difference of Squares} = 6^2 - 9^2 - 2^2 - 3^2 - 1^2 = 36 - 81 - 4 - 9 - 1 = -59 \)
Result: Difference of Squares = -59
2. Square of the Difference:
\( \text{Square of the Difference} = (6 - 9 - 2 - 3 - 1)^2 = (-9)^2 = 81 \)
Result: Square of the Difference = 81