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

less than a minute read Jun 16, 2024
(3x^2+5y^3)(3x^2-5y^3)

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.

Related Post


Featured Posts