(x-b)-answer.jpeg "(x+a)(x-b) Answer")
Expanding (x + a)(x - b)
The expression (x + a)(x - b) represents the product of two binomials. To find the answer, we can use the FOIL method, which stands for First, Outer, Inner, Last. Let's break down each step:
1. First:
Multiply the first terms of each binomial: x * x = x²
2. Outer:
Multiply the outer terms of the binomials: x * -b = -bx
3. Inner:
Multiply the inner terms of the binomials: a * x = ax
4. Last:
Multiply the last terms of each binomial: a * -b = -ab
Combining the Terms
Now, add all the terms together: x² - bx + ax - ab
Simplifying
Finally, we can combine the like terms (the terms with 'x') to get the final answer: x² + (a - b)x - ab
Therefore, the answer to (x + a)(x - b) is x² + (a - b)x - ab.
Example:
Let's apply this to a specific example: (x + 2)(x - 3)
Following the steps above:
- First: x * x = x²
- Outer: x * -3 = -3x
- Inner: 2 * x = 2x
- Last: 2 * -3 = -6
Combining the terms: x² - 3x + 2x - 6
Simplifying: x² - x - 6
This is the expanded form of (x + 2)(x - 3).
Conclusion
Expanding binomials using the FOIL method is a straightforward process that can be used to simplify expressions and solve various algebraic problems. Remember to combine like terms for a concise answer.