(x-b)-answer.jpeg "(x+a)(x-b) Answer")
Expanding the Product of (x+a) and (x-b)
In algebra, one of the most common and useful formulas is the expansion of the product of two binomials, specifically (x+a) and (x-b). This formula is widely used in various mathematical operations, such as simplifying expressions, solving equations, and graphing functions.
The Formula
The product of (x+a) and (x-b) is given by:
(x+a)(x-b) = x² - b² + a(x - b)
This formula can be derived by multiplying the two binomials using the distributive property of multiplication over addition.
Derivation
To derive the formula, we can start by multiplying the two binomials:
(x+a)(x-b) = x(x-b) + a(x-b)
= x² - xb + ax - ab
Now, we can combine like terms:
= x² - bx + ax - b²
= x² - b² + a(x - b)
Simplification
The resulting expression can be simplified further by combining the x terms:
= x² - b² + ax - ab
= x² - b² + x(a-b) - ab
Applications
The formula (x+a)(x-b) = x² - b² + a(x - b) has numerous applications in algebra and other branches of mathematics. Some examples include:
- Simplifying expressions: The formula can be used to simplify expressions involving the product of two binomials.
- Solving equations: The formula can be used to solve quadratic equations of the form
(x+a)(x-b) = 0. - Graphing functions: The formula can be used to graph quadratic functions in the form of
y = (x+a)(x-b).
Conclusion
In conclusion, the formula (x+a)(x-b) = x² - b² + a(x - b) is a fundamental concept in algebra that has numerous applications in mathematics. Understanding and applying this formula can help simplify complex expressions, solve equations, and graph functions.
