(x-b)-formula-class-9.jpeg "(x+a)(x-b) Formula Class 9")
Algebraic Identities: (x+a)(x-b) Formula for Class 9
In algebra, we often come across expressions that involve the product of two binomials. One such important formula is the (x+a)(x-b) formula. In this article, we will explore this formula, its expansion, and some examples to illustrate its application.
What is the (x+a)(x-b) Formula?
The (x+a)(x-b) formula is an algebraic identity that represents the product of two binomials. It is given by:
(x+a)(x-b) = x^2 + (a-b)x - ab
This formula is widely used in various mathematical operations, such as simplifying expressions, solving equations, and graphing functions.
Expansion of (x+a)(x-b)
To understand how this formula works, let's expand the product of (x+a) and (x-b):
(x+a)(x-b) = x(x-b) + a(x-b) = x^2 - xb + ax - ab = x^2 + (a-b)x - ab
As you can see, the expansion of (x+a)(x-b) yields a quadratic expression with three terms: x^2, (a-b)x, and -ab.
Examples of (x+a)(x-b) Formula
- Simplify the expression: (x+3)(x-2)
Using the (x+a)(x-b) formula, we get:
(x+3)(x-2) = x^2 + (3-2)x - (3)(2) = x^2 + x - 6
- Simplify the expression: (x+5)(x-1)
(x+5)(x-1) = x^2 + (5-1)x - (5)(1) = x^2 + 4x - 5
Applications of (x+a)(x-b) Formula
The (x+a)(x-b) formula has numerous applications in mathematics, physics, and engineering. Some of the areas where this formula is used include:
- Quadratic Equations: The formula is used to solve quadratic equations of the form
ax^2 + bx + c = 0. - Functions and Graphs: The formula is used to graph quadratic functions and analyze their properties.
- Algebraic Manipulations: The formula is used to simplify complex algebraic expressions and equations.
In conclusion, the (x+a)(x-b) formula is a powerful tool in algebra that has various applications in mathematics and other fields. By mastering this formula, you will be able to simplify expressions, solve equations, and graph functions with ease.
