(x-b)-formula-class-8.jpeg "(x-a)(x-b) Formula Class 8")
Understanding the (x-a)(x-b) Formula
In mathematics, the (x-a)(x-b) formula is a fundamental tool used to simplify and solve algebraic expressions. It is a special case of the distributive property and helps us expand products of binomials. Let's explore this formula in detail:
The Formula:
The (x-a)(x-b) formula states that the product of two binomials of the form (x-a) and (x-b) is equal to:
(x-a)(x-b) = x² - (a+b)x + ab
Expanding the Formula:
To understand how this formula works, let's break it down step by step:
- Multiply the first terms: x * x = x²
- Multiply the outer terms: x * (-b) = -bx
- Multiply the inner terms: (-a) * x = -ax
- Multiply the last terms: (-a) * (-b) = ab
- Combine the middle terms: -bx - ax = -(a+b)x
By combining all these terms, we arrive at the final expression: x² - (a+b)x + ab
Example:
Let's apply the formula to a specific example:
(x-2)(x-5)
Using the formula:
- a = 2, b = 5
- x² - (2+5)x + 2*5
- x² - 7x + 10
Therefore, (x-2)(x-5) expands to x² - 7x + 10.
Benefits of the Formula:
The (x-a)(x-b) formula provides several benefits:
- Simplifies algebraic expressions: It allows us to expand products of binomials quickly and efficiently.
- Facilitates factoring: It helps us factor quadratic expressions by recognizing the pattern.
- Essential for solving equations: It is a fundamental tool used in solving quadratic equations.
Conclusion:
The (x-a)(x-b) formula is an essential tool for students in Class 8 and beyond. Understanding this formula and its applications will provide a solid foundation for further mathematical learning and problem-solving. Practice using the formula with various examples to master its application and solidify your understanding of algebraic manipulation.