(x%2Bb)-answer.jpeg "(x+a)(x+b) Answer")
Expanding the Expression (x + a)(x + b)
The expression (x + a)(x + b) is a common algebraic expression that represents the product of two binomials. Expanding this expression involves multiplying each term in the first binomial by each term in the second binomial.
Using the FOIL Method
One common method for expanding this expression is the FOIL method:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * b = bx
- Inner: Multiply the inner terms of the binomials: a * x = ax
- Last: Multiply the last terms of each binomial: a * b = ab
Adding these products together, we get:
(x + a)(x + b) = x² + bx + ax + ab
Simplifying the Expression
The expanded expression can often be simplified by combining the terms with the same variable. In this case, the terms bx and ax both have the variable x. Combining these terms, we get:
(x + a)(x + b) = x² + (b + a)x + ab
Example
Let's expand the expression (x + 3)(x + 2) using the FOIL method:
- F: x * x = x²
- O: x * 2 = 2x
- I: 3 * x = 3x
- L: 3 * 2 = 6
Adding the products:
x² + 2x + 3x + 6
Combining like terms:
x² + 5x + 6
Conclusion
Expanding the expression (x + a)(x + b) using the FOIL method provides a straightforward way to multiply two binomials and obtain a simplified quadratic expression. This process is crucial in various algebraic manipulations and applications.