(x%2Bb)-formula-class-8.jpeg "(x+a)(x+b) Formula Class 8")
Understanding the (x + a)(x + b) Formula: A Guide for Class 8
The formula (x + a)(x + b) is a fundamental concept in algebra that allows us to simplify and solve equations. It is especially crucial in Class 8, where you begin to explore algebraic expressions and their manipulation. Let's break down this formula and understand how it works.
The Formula:
The formula (x + a)(x + b) states that the product of two binomials, each with a variable 'x' and constants 'a' and 'b', can be expanded as follows:
(x + a)(x + b) = x² + (a + b)x + ab
How it Works:
This formula is derived from the distributive property of multiplication. We simply multiply each term in the first binomial by each term in the second binomial:
- x * x = x²
- x * b = bx
- a * x = ax
- a * b = ab
Combining these terms, we get: x² + bx + ax + ab. Finally, we combine the like terms 'bx' and 'ax' to obtain the formula: x² + (a + b)x + ab.
Applications of the Formula:
The (x + a)(x + b) formula has various applications in algebra, including:
- Factoring quadratic equations: We can use this formula to factorize quadratic expressions by recognizing the pattern of the formula.
- Solving quadratic equations: By factoring the quadratic equations using the formula, we can find the roots (solutions) of the equation.
- Simplifying algebraic expressions: The formula helps us simplify expressions involving the product of binomials.
Example:
Let's see an example to illustrate how to use the formula:
Expand (x + 3)(x + 5)
Using the formula, we get:
(x + 3)(x + 5) = x² + (3 + 5)x + 3 * 5 = x² + 8x + 15
Conclusion:
The (x + a)(x + b) formula is a powerful tool in algebra that helps us understand and manipulate algebraic expressions. Understanding this formula is essential for Class 8 students as it lays the groundwork for more complex algebraic concepts.