(x+a)(x+b) Formula

3 min read Jun 17, 2024

Understanding the (x + a)(x + b) Formula

The (x + a)(x + b) formula is a fundamental concept in algebra, used to expand and simplify expressions involving the product of two binomials. This formula is also known as the "FOIL" method, which stands for First, Outer, Inner, Last, a mnemonic to remember the steps involved in the expansion.

Expanding the Expression

The formula states that:

(x + a)(x + b) = x² + (a + b)x + ab

This formula is derived by multiplying each term in the first binomial by each term in the second binomial:

First: x * x = x²
Outer: x * b = bx
Inner: a * x = ax
Last: a * b = ab

Combining the like terms, we get the final result: x² + (a + b)x + ab

Applying the Formula

The (x + a)(x + b) formula is used extensively in various algebraic operations such as:

Factoring quadratic expressions: This formula helps to factorize quadratic expressions by identifying the values of a and b.
Simplifying algebraic expressions: Expanding expressions with the formula allows for simplification by combining like terms.
Solving equations: The formula can be used to manipulate equations involving products of binomials.

Example

Let's expand the expression (x + 3)(x - 2) using the (x + a)(x + b) formula:

Here, a = 3 and b = -2.
Applying the formula: x² + (3 - 2)x + (3)(-2)
Simplifying: x² + x - 6

Therefore, (x + 3)(x - 2) = x² + x - 6

Conclusion

The (x + a)(x + b) formula is a powerful tool in algebra, allowing for the expansion and simplification of expressions involving the product of two binomials. Its wide application in various algebraic operations makes it a fundamental concept to master for understanding and manipulating algebraic expressions.