(x%2B5).jpeg "(x-2)(x+5)")
Expanding (x-2)(x+5)
This expression represents the product of two binomials: (x-2) and (x+5). To expand it, we can use the FOIL method:
First: Multiply the first terms of each binomial. Outer: Multiply the outer terms of the binomials. Inner: Multiply the inner terms of the binomials. Last: Multiply the last terms of each binomial.
Let's apply this to our expression:
- First: x * x = x²
- Outer: x * 5 = 5x
- Inner: -2 * x = -2x
- Last: -2 * 5 = -10
Now, we combine the terms:
x² + 5x - 2x - 10
Finally, we simplify by combining like terms:
x² + 3x - 10
Therefore, the expanded form of (x-2)(x+5) is x² + 3x - 10.
Understanding the Result
The expanded form represents a quadratic expression. This means it's a polynomial with the highest power of x being 2. The expression can be graphed as a parabola, which is a U-shaped curve.
The expanded form allows us to analyze the expression further, for example:
- Finding the roots: The roots of the equation x² + 3x - 10 = 0 represent the x-values where the parabola intersects the x-axis.
- Determining the vertex: The vertex of the parabola represents the minimum or maximum point of the function.
- Factoring the expression: The expanded form can be factored back into its original binomial form (x-2)(x+5).
By understanding the expanded form of (x-2)(x+5), we gain insights into the behavior of the expression and its various applications in mathematics and other fields.