(2a+b-5)(2a-b+5) Hằng Đẳng Thức

Jasonbradley

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Jun 16, 2024

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Understanding the Difference of Squares Pattern

The expression (2a + b - 5)(2a - b + 5) can be simplified using the difference of squares pattern, a fundamental concept in algebra.

The Difference of Squares Pattern

The difference of squares pattern states:

(x + y)(x - y) = x² - y²

This pattern shows that the product of two binomials, where one is the sum of two terms and the other is their difference, equals the square of the first term minus the square of the second term.

Applying the Pattern to the Expression

1. Identify the two terms: In our expression, we have two terms: (2a + b - 5) and (2a - b + 5).

2. Recognize the difference: Notice that the terms are identical except for the sign of the 'b' and '5' terms. This indicates we can apply the difference of squares pattern.

3. Apply the pattern:

   • Consider (2a + b - 5) as 'x' and (2a - b + 5) as 'y'.
   • Substitute into the pattern: (2a + b - 5)² - (2a - b + 5)²

4. Simplify:

   • Expanding the squares: (4a² + 4ab - 10a + b² - 10b + 25) - (4a² - 4ab + 10a + b² - 10b + 25)
   • Combine like terms: 4a² + 4ab - 10a + b² - 10b + 25 - 4a² + 4ab - 10a - b² + 10b - 25
   • The result: 8ab - 20a

Conclusion

By recognizing and applying the difference of squares pattern, we can simplify the expression (2a + b - 5)(2a - b + 5) to 8ab - 20a. This pattern is a powerful tool for simplifying expressions and solving algebraic equations.