(x-a)(x-b) Formula Example

Jasonbradley

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Jun 17, 2024

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

The formula (x - a)(x - b) is a fundamental concept in algebra, used to simplify and expand expressions. It is based on the distributive property, which states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.

The Formula:

(x - a)(x - b) = x² - (a + b)x + ab

Explanation:

• x²: This term comes from multiplying the 'x' terms in both brackets: x * x = x².
• -(a + b)x: This term comes from multiplying the 'x' term in the first bracket by the constant term in the second bracket, and vice versa: x * (-b) + (-a) * x = -(a + b)x.
• ab: This term comes from multiplying the constant terms in both brackets: (-a) * (-b) = ab.

Examples:

Example 1: Expand (x - 2)(x - 3)

1. Apply the formula: (x - 2)(x - 3) = x² - (2 + 3)x + 2 * 3
2. Simplify: x² - 5x + 6

Example 2: Expand (x + 5)(x - 1)

1. Rewrite: (x + 5)(x - 1) = (x - (-5))(x - 1)
2. Apply the formula: (x - (-5))(x - 1) = x² - (-5 + 1)x + (-5) * 1
3. Simplify: x² + 4x - 5

Applications:

This formula is commonly used in:

• Factoring quadratic expressions: You can use it to factor a quadratic expression into two linear factors.
• Solving quadratic equations: By factoring a quadratic equation using this formula, you can find the roots (solutions) of the equation.
• Simplifying algebraic expressions: This formula helps in simplifying complex expressions by expanding and combining like terms.

Remember:

The (x - a)(x - b) formula is a powerful tool for manipulating algebraic expressions. By understanding its components and applications, you can simplify and solve problems more efficiently.