Sum and Difference of Cubes
Special factoring patterns for cubes.
Key idea
Special factoring patterns for cubes.
In depth
a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²). The signs follow SOAP: Same, Opposite, Always Positive.
Worked example
x³ − 8 = (x − 2)(x² + 2x + 4).
Formula
Real-world uses
- Simplifying rational expressions in calculus and factoring volume-based formulas
Common mistake
Writing the wrong sign in the middle term or trying to factor the quadratic part further.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Sum and Difference of Cubes?
Special factoring patterns for cubes. It is a topic at the advanced level in Algebra.
What is the formula for Sum and Difference of Cubes?
The key formula is a³±b³ = (a±b)(a²∓ab+b²).
Where is Sum and Difference of Cubes used in real life?
Real-world examples: Simplifying rational expressions in calculus and factoring volume-based formulas.
What should I learn before Sum and Difference of Cubes?
Make sure you are comfortable with Difference of Squares, the previous topic in Algebra.
What is a common mistake with Sum and Difference of Cubes?
Writing the wrong sign in the middle term or trying to factor the quadratic part further.
How can I practise Sum and Difference of Cubes?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Sum and Difference of Cubes?
Move on to Quadratic Equations by Factoring next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.
- Quadratic Formula – Gives roots of any quadratic.