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

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (3x+5y)² - (3x-5y)²

This expression involves squaring binomials and subtracting the results. We can simplify this using the difference of squares pattern:

Difference of Squares Pattern: a² - b² = (a + b)(a - b)

Let's apply this pattern to our expression:

1. Identify 'a' and 'b':

   • a = (3x + 5y)
   • b = (3x - 5y)

2. Substitute into the pattern:

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

3. Simplify the expression:

   • [(3x + 5y) + (3x - 5y)][(3x + 5y) - (3x - 5y)] = (6x)(10y) = 60xy

Therefore, the simplified form of (3x+5y)² - (3x-5y)² is 60xy.