(3x^2+5y^3)(3x^2-5y^3)

Jasonbradley

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Jun 16, 2024

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Factoring the Difference of Squares: (3x² + 5y³) (3x² - 5y³)

This expression represents a classic example of the difference of squares factorization pattern. Here's how it works:

Understanding the Pattern

The difference of squares pattern states: a² - b² = (a + b)(a - b)

Applying the Pattern

1. Identify the squares:

   • In our expression, (3x²) is the square of (3x).
   • (5y³) is the square of (5y).

2. Apply the pattern:

   • (3x² + 5y³) (3x² - 5y³) = [(3x)² + (5y)³][(3x)² - (5y)³]

3. Simplify:

   • This directly follows the difference of squares pattern, resulting in:
   • (3x)² - (5y)³ = 9x⁴ - 25y⁶

Therefore, the factored form of (3x² + 5y³) (3x² - 5y³) is 9x⁴ - 25y⁶.

Key Takeaways

• The difference of squares pattern is a powerful tool for simplifying algebraic expressions.
• Recognizing the pattern can save time and effort when factoring.
• This pattern is applicable in various mathematical contexts, including solving equations and simplifying expressions.