Sum & Difference of Cubes Game

Sum & Difference of Cubes Game
This game is designed to help you master the Sum and Difference of Cubes factoring formulas through rapid-fire practice.Scroll down for a detailed explanation.
 

 

How to Play the Sum & Difference of Cubes Game
The Formulas
Sum of Cubes: a³ + b³ = (a + b)(a² - ab + b²)
Difference of Cubes: a³ - b³ = (a - b)(a² + ab + b²)

1. Choose Your Mode
   On the main menu, select how you want to play:
   Sum of Cubes: Only problems with the plus sign (x³ + 27).
   Difference of Cubes: Only problems with the minus sign (x³ - 8).
   Mixed Protocol: A random mix of both (recommended for building real fluency).
   

2. Identify the Cube Root (b)
   When the game starts, you will see a “Target Expression.” You need to identify the cube root of the number shown.
   If you see 8, your b value is 2 (2 × 2 × 2 = 8).
   If you see 27, your b value is 3 (3 × 3 × 3 = 27).
   If you see 64, your b value is 4 (4 × 4 × 4 = 64).
   

3. Apply the SOAP Rule
   To get the signs right every time, remember the SOAP acronym. This determines the signs for the three spaces in the formula: (a [S] b)(a² [O] ab [AP] b²).
   S (Same): The sign in the small parentheses is the same as the original problem.
   O (Opposite): The first sign in the large parentheses is the opposite of the original.
   AP (Always Positive): The last sign is always positive.
   

4. Input the Factored Form
   You must type the factors into the two boxes without spaces.
   Example Problem: x³ + 125
   Cube root: b = 5.
   Binomial (Small Box): Type x+5 (The Same sign as +).
   Trinomial (Large Box): Type x²-5x+25 (The Opposite sign -, then 5 times x, then 5²).
   

Example Problem: x³ - 27
Cube root: b = 3.
Binomial: Type x-3 (The Same sign as -).
Trinomial: Type x²+3x+9 (The Opposite sign +, then 3 times x, then 3²).

5. Scoring & Feedback
   Validate: Click the button to check your answer.
   Sync Status: Your score is tracked at the top.
   Error Correction: If you get it wrong, check your signs (SOAP) or make sure you squared the b value at the end of the trinomial.
   

This video gives a clear, step-by-step approach to factor sum and difference of cubes.

• Show Video

 

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