(x-b)-formula-class-8.jpeg "(x+a)(x-b) Formula Class 8")
Understanding the (x + a)(x - b) Formula: A Class 8 Guide
In algebra, we often encounter expressions in the form of (x + a)(x - b). This expression represents the product of two binomials, and understanding how to expand it is crucial for solving various problems.
What is the (x + a)(x - b) Formula?
The (x + a)(x - b) formula is a shortcut for multiplying two binomials where one binomial has a positive term and the other has a negative term. It states that:
(x + a)(x - b) = x² - (b - a)x - ab
Let's break down how this formula works:
1. First terms: Multiply the first terms of each binomial: x * x = x²
2. Outer terms: Multiply the outer terms of the binomials: x * -b = -bx
3. Inner terms: Multiply the inner terms of the binomials: a * x = ax
4. Last terms: Multiply the last terms of each binomial: a * -b = -ab
5. Combine: Add the terms together: x² - bx + ax - ab
6. Simplify: Combine the like terms (the terms with 'x') to get the final expression: x² - (b - a)x - ab
Applying the Formula
Let's look at an example to illustrate how the formula works:
(x + 3)(x - 5)
Using the formula:
- x²: (x * x) = x²
- -(b - a)x: - (5 - 3)x = -2x
- -ab: - (3 * 5) = -15
Therefore, (x + 3)(x - 5) = x² - 2x - 15
Benefits of the Formula
- Efficiency: The formula provides a quick and easy way to multiply binomials of this form.
- Accuracy: It ensures that you don't miss any terms when expanding the expression.
- Foundation: Understanding this formula helps you with more complex algebraic manipulations later on.
Practice Makes Perfect!
The best way to master the (x + a)(x - b) formula is by practicing. Try expanding different expressions of this form using the formula and comparing your answers with the results obtained by direct multiplication.
With consistent practice, you'll be able to apply this formula confidently and efficiently in your algebraic calculations!