(x-b)-formula-class-9.jpeg "(x+a)(x-b) Formula Class 9")
The (x+a)(x-b) Formula: A Key to Simplifying Algebraic Expressions
In mathematics, the (x+a)(x-b) formula is a powerful tool that helps us simplify expressions involving the product of two binomials. It's particularly useful for expanding and simplifying expressions in algebra, a crucial skill for students in Class 9 and beyond.
Understanding the Formula
The formula states that:
(x + a)(x - b) = x² - (b - a)x - ab
Let's break down this formula:
- x²: This term is obtained by multiplying the first terms of each binomial (x * x).
- -(b - a)x: This term arises from the sum of the products of the outer terms and the inner terms of the binomials ((x * -b) + (a * x)).
- -ab: This term results from multiplying the last terms of each binomial (a * -b).
Applying the Formula
To apply this formula, simply substitute the values of a and b into the formula. For example, let's expand the expression (x + 3)(x - 2) using the formula.
- Identify a and b: Here, a = 3 and b = 2.
- Substitute the values: x² - (2 - 3)x - (3 * 2)
- Simplify: x² + x - 6
Therefore, the expanded form of (x + 3)(x - 2) is x² + x - 6.
Benefits of Using the Formula
- Efficiency: The formula provides a shortcut for expanding expressions without having to manually multiply each term.
- Accuracy: It eliminates the possibility of errors that may arise from manual multiplication.
- Versatility: The formula can be applied to any expression of the form (x + a)(x - b).
Examples
Here are some more examples of how to use the formula:
- (x + 5)(x - 1): x² - (1 - 5)x - (5 * 1) = x² + 4x - 5
- (x - 4)(x + 7): x² - (7 + 4)x - (-4 * 7) = x² - 11x + 28
Conclusion
The (x+a)(x-b) formula is a valuable tool for simplifying algebraic expressions. Understanding and applying this formula can significantly enhance your ability to manipulate algebraic equations and solve problems more efficiently. It's an essential part of your mathematical toolkit as you progress through Class 9 and beyond.