(3x+5y)^2-4z^2

Jasonbradley

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Jun 16, 2024

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Factoring the Expression: (3x + 5y)² - 4z²

The expression (3x + 5y)² - 4z² can be factored using the difference of squares pattern.

Difference of Squares Pattern

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

Applying the Pattern

1. Identify a and b:

   • In our expression, a = (3x + 5y) and b = 2z.

2. Substitute into the pattern:

   • (3x + 5y)² - 4z² = [(3x + 5y) + 2z][(3x + 5y) - 2z]

3. Simplify:

   • (3x + 5y + 2z)(3x + 5y - 2z)

Final Factored Form

Therefore, the factored form of (3x + 5y)² - 4z² is (3x + 5y + 2z)(3x + 5y - 2z).