Solving a Sum of Cubes Equation

Question:
Solve for x: x cubed equals 30 cubed plus 40 cubed plus 50 cubed.

Solving a Sum of Cubes Equation

This lesson solves the equation x³ = 30³ + 40³ + 50³ by factoring out a common base and recognizing a perfect cube. Students discover the elegant identity 3³ + 4³ + 5³ = 6³ and apply properties of cube roots to find the solution.

In this lesson, you will learn to:
• Factor a common base from a sum of cubes to simplify expressions
• Recognize and apply the identity 3³ + 4³ + 5³ = 6³
• Use the property (a · b)³ = a³ · b³ to combine factors
• Solve an equation of the form x³ = k by taking cube roots

Course: Calculus
Level: Grade 9

Pause before each step, try the next part yourself, and then continue to check your reasoning.

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