Difference of Cubes and Cube of Difference Calculator

Enter a set of data to calculate the difference of cubes and the cube of the difference.

Calculate the Difference of Cubes and Cube of Difference

Difference of Cubes

Cube of Difference

How to Calculate the Difference of Cubes and the Cube of the Differenc

1. Difference of Cubes

The difference of cubes refers to cubing each number in a set and then subtracting the results. For a set of numbers \( X, Y, Z \), the formula for the difference of cubes is: \( \text{Difference of Cubes} = X^3 - Y^3 - Z^3 \) This formula can be applied to any number of values, where each value is cubed and then subtracted, used to analyze the cubic differences between numbers.

2. Cube of the Difference

The cube of the difference refers to first calculating the difference between the numbers in a set, and then cubing the result. For a set of numbers \( X, Y, Z \), the formula for the cube of the difference is: \( \text{Cube of the Difference} = (X - Y - Z)^3 \) This formula first calculates the difference between the numbers and then cubes the result, reflecting the cubic difference between the data.

Custom Delimiters Explanation

The Difference of Cubes and Cube of Difference Calculator can automatically handle common delimiters such as commas, spaces, semicolons, line breaks, etc. Users can also enter a custom delimiter (e.g., "|" ) if needed. The calculator allows for a thousand separator, but note that the thousand separator and number separator must be different to ensure accurate calculations.

Examples

Example 1: For the data set \( [10, 6, 3] \), calculate the difference of cubes and the cube of the difference.

Solution:

1. Difference of Cubes:

\( 10^3 - 6^3 - 3^3 = 1000 - 216 - 27 = 757 \)

Result: Difference of Cubes = 757

2. Cube of the Difference:

\( (10 - 6 - 3)^3 = (1)^3 = 1 \)

Result: Cube of the Difference = 1

Example 2: For the data set \( [100, 50, 40, 30] \), calculate the difference of cubes and the cube of the difference.

Solution:

1. Difference of Cubes:

\( 100^3 - 50^3 - 40^3 - 30^3 = 1000000 - 125000 - 64000 - 27000 = 784000 \)

Result: Difference of Cubes = 784000

2. Cube of the Difference:

\( (100 - 50 - 40 - 30)^3 = (-20)^3 = -8000 \)

Result: Cube of the Difference = -8000

Example 3: For the data set \( [15, 9, 2, 5, 3] \), calculate the difference of cubes and the cube of the difference.

Solution:

1. Difference of Cubes:

\( 15^3 - 9^3 - 2^3 - 5^3 - 3^3 = 3375 - 729 - 8 - 125 - 27 = 2486 \)

Result: Difference of Cubes = 2486

2. Cube of the Difference:

\( (15 - 9 - 2 - 5 - 3)^3 = (-4)^3 = -64 \)

Result: Cube of the Difference = -64