(x-1)-expand-and-simplify.jpeg "(x+1)(x-1) Expand And Simplify")
Expanding and Simplifying (x+1)(x-1)
In mathematics, expanding and simplifying expressions is a fundamental skill. Let's look at how to expand and simplify the expression (x+1)(x-1).
Understanding the Process
Expanding an expression means multiplying out the brackets. We can use the FOIL method (First, Outer, Inner, Last) to achieve this:
- First: Multiply the first terms of each bracket: x * x = x²
- Outer: Multiply the outer terms of the brackets: x * -1 = -x
- Inner: Multiply the inner terms of the brackets: 1 * x = x
- Last: Multiply the last terms of each bracket: 1 * -1 = -1
This gives us: x² - x + x - 1
Simplifying the Expression
Now, we need to combine like terms:
- The terms -x and x cancel each other out.
This leaves us with the simplified expression: x² - 1
Conclusion
Therefore, expanding and simplifying the expression (x+1)(x-1) results in x² - 1. This simplified form is often easier to work with in algebraic manipulations and calculations.