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

less than a minute read Jun 16, 2024
(3/2m+2/3n)(3/2m-2/3n)

Simplifying the Expression (3/2m + 2/3n)(3/2m - 2/3n)

This expression represents the product of two binomials, which can be simplified using the difference of squares pattern.

Understanding the Difference of Squares Pattern

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

Applying the Pattern

In our expression, let's identify 'a' and 'b':

  • a = 3/2m
  • b = 2/3n

Now, we can substitute these values into the difference of squares pattern:

(3/2m + 2/3n)(3/2m - 2/3n) = (3/2m)² - (2/3n)²

Simplifying the Expression

Finally, we simplify the squares:

(3/2m)² - (2/3n)² = 9/4m² - 4/9n²

Conclusion

Therefore, the simplified form of the expression (3/2m + 2/3n)(3/2m - 2/3n) is 9/4m² - 4/9n².

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