(x-b)-formula-class-9.jpeg "(x-a)(x-b) Formula Class 9")
Formula for (x-a)(x-b) in Class 9
In algebra, we often come across expressions involving the product of two binomials. One such important formula is the formula for (x-a)(x-b). In this article, we will learn about this formula, its derivation, and some examples to illustrate its application.
Derivation of the Formula
To derive the formula for (x-a)(x-b), let's start by multiplying the two binomials:
(x-a)(x-b) = ?
We can multiply each term in the first binomial with each term in the second binomial:
= x(x-b) - a(x-b) = x^2 - bx - ax + ab = x^2 - (a+b)x + ab
This is the formula for (x-a)(x-b). By using this formula, we can easily expand the product of two binomials.
Examples
Example 1
Find the value of (x-2)(x-3).
Using the formula, we get:
= x^2 - (2+3)x + 2*3 = x^2 - 5x + 6
Example 2
Find the value of (x+1)(x-4).
Using the formula, we get:
= x^2 - (1-4)x + 1*(-4) = x^2 + 3x - 4
Importance of the Formula
This formula is widely used in various mathematical problems, such as:
- Factoring quadratic expressions: The formula can be used to factorize quadratic expressions of the form ax^2 + bx + c.
- Solving quadratic equations: The formula can be used to solve quadratic equations of the form ax^2 + bx + c = 0.
- Algebraic manipulations: The formula can be used to simplify algebraic expressions involving the product of two binomials.
Conclusion
In conclusion, the formula for (x-a)(x-b) is a powerful tool in algebra that can be used to expand the product of two binomials. By mastering this formula, you can solve a wide range of mathematical problems with ease.
