(x-b)-formula-class-9.jpeg "(x-a)(x-b) Formula Class 9")
Understanding the (x-a)(x-b) Formula: A Class 9 Guide
The formula (x-a)(x-b) = x² - (a+b)x + ab is a fundamental concept in algebra, particularly for students in Class 9. It's a shortcut for expanding a product of two binomials, and it simplifies the process of multiplying expressions. Here's a breakdown of what it means and how to apply it:
What is the (x-a)(x-b) Formula?
This formula essentially states that the product of two binomials, where each binomial is in the form (x-a) and (x-b), can be expanded into a trinomial. Let's break down the formula:
- x²: This term is obtained by multiplying the 'x' terms from both binomials.
- -(a+b)x: This term is the sum of the products of the 'x' term in one binomial and the constant term in the other binomial.
- ab: This term is the product of the constant terms from both binomials.
Why is this Formula Important?
This formula serves as a shortcut for simplifying and manipulating algebraic expressions. It allows you to quickly expand binomials without having to go through the tedious process of multiplying each term individually. This is especially helpful when dealing with complex expressions involving multiple variables and constants.
Applying the Formula: A Step-by-Step Guide
- Identify the 'a' and 'b' values: In the formula (x-a)(x-b), the constants 'a' and 'b' represent the values being subtracted from 'x' in each binomial.
- Find the sum of 'a' and 'b': Add the values of 'a' and 'b' together.
- Find the product of 'a' and 'b': Multiply the values of 'a' and 'b' together.
- Substitute the values into the formula: Replace 'a+b' and 'ab' in the formula with the values you calculated in steps 2 and 3.
- Simplify the expression: Combine like terms to obtain the simplified trinomial.
Example:
Let's say we want to expand the expression (x-2)(x-3).
- a = 2 and b = 3
- a + b = 2 + 3 = 5
- ab = 2 * 3 = 6
- x² - (a+b)x + ab = x² - 5x + 6
Therefore, (x-2)(x-3) = x² - 5x + 6.
Conclusion
The (x-a)(x-b) formula is a powerful tool for simplifying algebraic expressions. By understanding this formula, you can expand binomials with ease and gain a deeper understanding of algebraic manipulation. Mastering this formula is essential for success in Class 9 and beyond.