(x%2Bb)-formula-class-9.jpeg "(x+a)(x+b) Formula Class 9")
Algebraic Identities: (x+a)(x+b) Formula for Class 9
Algebraic identities are equations that are true for all values of variables. In this article, we will learn about one of the most important algebraic identities, which is the (x+a)(x+b) formula.
What is the (x+a)(x+b) Formula?
The (x+a)(x+b) formula is an algebraic identity that states:
(x+a)(x+b) = x² + (a+b)x + ab
This formula is used to expand the product of two binomials. A binomial is an expression with two terms, such as x+a and x+b.
How to Derive the (x+a)(x+b) Formula?
To derive the (x+a)(x+b) 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 the like terms:
(x+a)(x+b) = x² + (a+b)x + ab
Thus, we have derived the (x+a)(x+b) formula.
Examples and Applications
Let's see how to apply the (x+a)(x+b) formula to some examples:
Example 1: Expand (x+2)(x+3) using the (x+a)(x+b) formula.
(x+2)(x+3) = x² + (2+3)x + (2)(3)
= x² + 5x + 6
Example 2: Expand (x-4)(x+1) using the (x+a)(x+b) formula.
(x-4)(x+1) = x² + (-4+1)x + (-4)(1)
= x² - 3x - 4
The (x+a)(x+b) formula has many applications in algebra, geometry, and other branches of mathematics.
Importance of the (x+a)(x+b) Formula
The (x+a)(x+b) formula is an essential tool in algebra and is used in many mathematical concepts, such as:
- Expanding products of binomials
- Factoring quadratic expressions
- Solving quadratic equations
- Graphing quadratic functions
In conclusion, the (x+a)(x+b) formula is a fundamental algebraic identity that is used to expand the product of two binomials. It has many applications in mathematics and is an essential tool for problem-solving.
