%5E2.jpeg "(x+5/2)^2")
Understanding (x + 5/2)²
The expression (x + 5/2)² represents the square of the binomial (x + 5/2). This means we are multiplying the binomial by itself:
(x + 5/2)² = (x + 5/2) * (x + 5/2)
To simplify this expression, we can use the FOIL method:
- First: x * x = x²
- Outer: x * 5/2 = 5x/2
- Inner: 5/2 * x = 5x/2
- Last: 5/2 * 5/2 = 25/4
Now we can combine the terms:
x² + 5x/2 + 5x/2 + 25/4 = x² + 5x + 25/4
Simplifying the Expression:
The simplified expression x² + 5x + 25/4 represents a quadratic equation. This equation can be further manipulated for various applications, including:
- Finding the roots: The roots of this quadratic equation are the values of x that make the expression equal to zero.
- Graphing: The expression represents a parabola that opens upwards.
- Solving equations: This expression can be used in solving equations where the unknown variable is squared.
Key Points:
- The expression (x + 5/2)² is a perfect square trinomial.
- The FOIL method is a helpful tool for expanding binomials.
- The simplified expression can be used in various mathematical contexts.
Understanding the properties and manipulation of the expression (x + 5/2)² is essential for solving problems involving quadratic equations, graphing parabolas, and other mathematical concepts.