(2m+3n)^2-(3m+2n)^2

Jasonbradley

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Jun 16, 2024

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Factoring the Difference of Squares: (2m + 3n)² - (3m + 2n)²

This problem involves the difference of squares, a common pattern in algebra. Here's how to solve it:

Understanding the 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 = (2m + 3n) and b = (3m + 2n)

2. Substitute into the pattern:

   • (2m + 3n)² - (3m + 2n)² = [(2m + 3n) + (3m + 2n)][(2m + 3n) - (3m + 2n)]

3. Simplify:

   • [(2m + 3n) + (3m + 2n)][(2m + 3n) - (3m + 2n)] = (5m + 5n)(-m + n)

Final Answer:

Therefore, (2m + 3n)² - (3m + 2n)² = (5m + 5n)(-m + n)

Important Note: You can further factor out a 5 from the first term to get: 5(m + n)(-m + n)