(3a-4b)-(2a-5b)(2a%2B5b).jpeg "(3a+4b)(3a-4b)-(2a-5b)(2a+5b)")
Simplifying the Expression: (3a + 4b)(3a - 4b) - (2a - 5b)(2a + 5b)
This expression involves the product of two binomials, and we can simplify it using the difference of squares pattern.
The Difference of Squares
The difference of squares pattern states that: (x + y)(x - y) = x² - y²
Applying the Pattern
Let's break down the given expression:
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(3a + 4b)(3a - 4b): This is in the form (x + y)(x - y), where x = 3a and y = 4b. Using the difference of squares pattern, this simplifies to (3a)² - (4b)² = 9a² - 16b².
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(2a - 5b)(2a + 5b): Similarly, this is in the form (x - y)(x + y), where x = 2a and y = 5b. This simplifies to (2a)² - (5b)² = 4a² - 25b².
Combining the Results
Now, our original expression becomes: (3a + 4b)(3a - 4b) - (2a - 5b)(2a + 5b) = (9a² - 16b²) - (4a² - 25b²)
Simplifying Further
Distributing the negative sign and combining like terms: 9a² - 16b² - 4a² + 25b² = 5a² + 9b²
Conclusion
Therefore, the simplified form of the expression (3a + 4b)(3a - 4b) - (2a - 5b)(2a + 5b) is 5a² + 9b².