(3%2F2m-2%2F3n).jpeg "(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.