Sum and Difference of Cubes Factorization Calculator
Unravel algebraic expressions of the form $$a^3 \pm b^3$$ into their factored forms with ease.
Factorization Inputs
Enter the terms and choose the operation to factorize.
a³
b³
Factored Form:
Calculation Steps:
Understanding Sum and Difference of Cubes Factorization
Sum and Difference of Cubes are special algebraic identities used to factorize expressions of the form $$a^3 + b^3$$ and $$a^3 - b^3$$. These formulas simplify complex expressions into products of simpler factors, making them easier to analyze and solve.
Formulas:
- Sum of Cubes: $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$
- Difference of Cubes: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$
How to Use This Tool:
To factorize an expression:
- Enter the value of the first term (a³) in the 'First term (a³)' input box.
- Enter the value of the second term (b³) in the 'Second term (b³)' input box.
- Select the operation ('+' for sum, '-' for difference) from the dropdown.
- Click the 'Factorize' button to calculate the factored form.
- The factored expression will be displayed, and you can copy it to your clipboard.
- Optionally, click 'Show Steps' to view the step-by-step calculation process.
This tool is helpful for students learning algebra, engineers, and anyone who needs to quickly factorize cubic expressions.
Learn more about Sum and Difference of Cubes on Wikipedia.