(x-5).jpeg "(x-4)(x-5)")
Expanding and Simplifying (x-4)(x-5)
This expression represents the product of two binomials: (x - 4) and (x - 5). To expand and simplify it, we can use the FOIL method:
First: Multiply the first terms of each binomial: x * x = x² Outer: Multiply the outer terms: x * -5 = -5x Inner: Multiply the inner terms: -4 * x = -4x Last: Multiply the last terms: -4 * -5 = 20
Now, we combine the terms:
x² - 5x - 4x + 20
Finally, we simplify by combining like terms:
x² - 9x + 20
Therefore, the expanded and simplified form of (x-4)(x-5) is x² - 9x + 20.
Understanding the Result
The expression x² - 9x + 20 represents a quadratic equation. This equation can be used to model various real-world situations.
For example:
- Projectile motion: The height of a ball thrown vertically can be modeled by a quadratic equation, where the x-term represents time and the y-term represents height.
- Area calculations: The area of a rectangular plot of land can be represented by a quadratic equation, where the x-term represents the length and the y-term represents the width.
By understanding the expanded and simplified form of (x-4)(x-5), we can analyze and solve problems related to quadratic equations.