(x-b)-formula-example.jpeg "(x+a)(x-b) Formula Example")
Understanding the (x + a)(x - b) Formula: A Simple Guide
The formula (x + a)(x - b) is a fundamental concept in algebra, used to simplify and solve various equations. It's a special case of the difference of squares pattern, which states:
(a + b)(a - b) = a² - b²
In our case, 'a' is represented by 'x + a' and 'b' is represented by 'x - b'. Let's break down this formula and see how it works.
Applying the Formula
To understand how the formula works, let's apply it to an example:
(x + 3)(x - 2)
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Identify 'a' and 'b':
- a = x + 3
- b = x - 2
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Apply the difference of squares pattern:
- (x + 3)² - (x - 2)²
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Expand the squares:
- (x² + 6x + 9) - (x² - 4x + 4)
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Simplify by combining like terms:
- x² + 6x + 9 - x² + 4x - 4
- 10x + 5
Therefore, (x + 3)(x - 2) = 10x + 5
Key Benefits of the Formula
The (x + a)(x - b) formula offers several advantages:
- Efficiency: It simplifies complex expressions quickly, saving time and effort.
- Generalizability: The pattern applies to various algebraic expressions, making it versatile.
- Understanding of Quadratic Expressions: It helps in recognizing and factoring quadratic expressions.
Real-World Applications
This formula has practical applications in various fields:
- Physics: Calculating work done by a force.
- Engineering: Designing structures and analyzing forces.
- Finance: Calculating compound interest and loan payments.
Conclusion
The (x + a)(x - b) formula is a powerful tool in algebra, enabling us to simplify expressions and solve equations efficiently. By understanding this formula and its applications, we can tackle more complex problems in various areas of study and daily life.