(x-b)-formula-example.jpeg "(x+a)(x-b) Formula Example")
(x+a)(x-b) Formula: Expansion and Examples
The (x+a)(x-b) formula is a fundamental concept in algebra, used to expand and simplify expressions involving binomials. In this article, we will delve into the formula, its expansion, and provide examples to illustrate its application.
The Formula:
The (x+a)(x-b) formula is a product of two binomials, (x+a) and (x-b). The formula can be written as:
(x+a)(x-b) = x^2 - b^2 + a(x-b)
Expansion:
To expand the formula, we need to follow the order of operations (PEMDAS):
- Multiply the two binomials:
(x+a)(x) = x^2 + ax(x+a)(-b) = -bx - ab
- Combine like terms:
x^2 + ax - bx - ab
- Simplify the expression:
x^2 - b^2 + a(x-b)
Examples:
Example 1:
Expand (x+3)(x-2)
Using the formula, we get:
(x+3)(x-2) = x^2 - 2^2 + 3(x-2)
= x^2 - 4 + 3x - 6
Simplifying the expression, we get:
= x^2 + 3x - 10
Example 2:
Expand (x-5)(x+2)
Using the formula, we get:
(x-5)(x+2) = x^2 - 2^2 - 5(x+2)
= x^2 - 4 - 5x - 10
Simplifying the expression, we get:
= x^2 - 5x - 14
Real-World Applications:
The (x+a)(x-b) formula has numerous applications in various fields, including:
- Physics: Expanding binomials is essential in calculating energies, velocities, and accelerations.
- Engineering: The formula is used in designing electronic circuits, bridges, and buildings.
- Computer Science: Binomial expansions are crucial in developing algorithms and programming languages.
Conclusion:
The (x+a)(x-b) formula is a powerful tool in algebra, enabling us to expand and simplify complex expressions. By mastering this formula, you'll be well-equipped to tackle a wide range of mathematical problems and applications.
