(2x+3y)3-(2x-3y)3

Jasonbradley

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Jun 16, 2024

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Expanding (2x + 3y)³ - (2x - 3y)³

This expression involves the difference of two cubes, a common pattern in algebra. We can use a specific formula to simplify the expression:

Formula: a³ - b³ = (a - b)(a² + ab + b²)

Applying the formula to our expression:

• Let a = 2x + 3y
• Let b = 2x - 3y

Now, we can substitute these values into the formula:

[(2x + 3y) - (2x - 3y)][(2x + 3y)² + (2x + 3y)(2x - 3y) + (2x - 3y)²]

Simplifying:

1. Simplify the first factor: (2x + 3y) - (2x - 3y) = 6y

2. Expand the second factor:

   • (2x + 3y)² = 4x² + 12xy + 9y²
   • (2x + 3y)(2x - 3y) = 4x² - 9y²
   • (2x - 3y)² = 4x² - 12xy + 9y²

3. Combine the terms: 6y [4x² + 12xy + 9y² + 4x² - 9y² + 4x² - 12xy + 9y²]

4. Simplify: 6y [12x² + 9y²]

Final answer: 36x²y + 54y³

Therefore, the expanded form of (2x + 3y)³ - (2x - 3y)³ is 36x²y + 54y³.