(x-5).jpeg "(x+2)(x-5)")
Expanding the Expression: (x+2)(x-5)
The expression (x+2)(x-5) is a product of two binomials. To expand this expression, we can use the FOIL method, which stands for First, Outer, Inner, Last.
Steps to Expand:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -5 = -5x
- Inner: Multiply the inner terms of the binomials: 2 * x = 2x
- Last: Multiply the last terms of the binomials: 2 * -5 = -10
Now, combine all the terms: x² - 5x + 2x - 10
Finally, simplify by combining like terms: x² - 3x - 10
Therefore, the expanded form of (x+2)(x-5) is x² - 3x - 10.
Factoring the Expression:
We can also reverse the process and factor the expression x² - 3x - 10 to get back to (x+2)(x-5). This involves finding two numbers that add up to -3 (the coefficient of the x term) and multiply to -10 (the constant term). In this case, the numbers are -5 and 2.
Applications:
This expression can be used in various mathematical applications, including:
- Solving quadratic equations: Setting the expression equal to zero and solving for x will give you the roots of the quadratic equation.
- Graphing parabolas: The expression represents a parabola, and expanding it allows you to easily determine its vertex and intercepts.
- Calculus: The expression can be used in differentiation and integration problems.
Expanding and factoring expressions like (x+2)(x-5) is a fundamental skill in algebra and is essential for understanding and solving various mathematical problems.