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Expanding (x+a)(x-b) Examples
In algebra, expanding the product of two binomials is an essential skill. One of the most common examples is expanding (x+a)(x-b). In this article, we will provide examples and explanations on how to expand this type of expression.
What is (x+a)(x-b)?
(x+a)(x-b) is a product of two binomials, where x is a variable, and a and b are constants. To expand this expression, we need to multiply each term in the first binomial by each term in the second binomial.
The Formula
The formula to expand (x+a)(x-b) is:
(x+a)(x-b) = x^2 - bx + ax - ab
Examples
Example 1: Expand (x+3)(x-2)
To expand this expression, we substitute a = 3 and b = 2 into the formula:
(x+3)(x-2) = x^2 - 2x + 3x - 6 = x^2 + x - 6
Example 2: Expand (x+5)(x-1)
Substituting a = 5 and b = 1 into the formula, we get:
(x+5)(x-1) = x^2 - x + 5x - 5 = x^2 + 4x - 5
Example 3: Expand (x-2)(x+4)
In this example, we have a = -2 and b = 4. Plugging these values into the formula, we get:
(x-2)(x+4) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8
Conclusion
Expanding (x+a)(x-b) is a fundamental skill in algebra. By following the formula and substituting the correct values, you can expand these types of expressions with ease. Practice these examples to become proficient in expanding (x+a)(x-b) and you'll be ready to tackle more complex algebraic expressions.
