(x-1).jpeg "(x+2)(x-1)")
Expanding and Simplifying (x+2)(x-1)
In mathematics, we often encounter expressions like (x+2)(x-1) which involve the product of two binomials. To simplify these expressions, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last, which refers to the order in which we multiply the terms of the binomials:
1. First: Multiply the first terms of each binomial:
- x * x = x²
2. Outer: Multiply the outer terms of the binomials:
- x * -1 = -x
3. Inner: Multiply the inner terms of the binomials:
- 2 * x = 2x
4. Last: Multiply the last terms of each binomial:
- 2 * -1 = -2
Now, we have: x² - x + 2x - 2
5. Simplify: Combine the like terms (-x + 2x):
- x² + x - 2
Therefore, the expanded and simplified form of (x+2)(x-1) is x² + x - 2.
Why is FOIL Important?
The FOIL method helps us to systematically multiply binomials and avoid missing any terms. It's a crucial technique for simplifying expressions, solving equations, and understanding polynomial functions.
Further Applications
The expanded form of (x+2)(x-1) can be used in various ways, including:
- Factoring Quadratics: The expression can be factored back into (x+2)(x-1).
- Solving Equations: Setting the expression equal to zero and solving for x allows us to find the roots of the quadratic equation.
- Graphing Functions: The expression represents a parabola when plotted on a graph.
Understanding how to expand and simplify binomials is a fundamental skill in algebra and has wide applications in various mathematical concepts.