(x-9).jpeg "(x+10)(x-9)")
Expanding (x+10)(x-9)
The expression (x+10)(x-9) is a product of two binomials. To expand this expression, we can use the FOIL method, which stands for First, Outer, Inner, Last.
Here's how it works:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -9 = -9x
- Inner: Multiply the inner terms of the binomials: 10 * x = 10x
- Last: Multiply the last terms of the binomials: 10 * -9 = -90
Now, combine the results:
x² - 9x + 10x - 90
Finally, simplify by combining like terms:
x² + x - 90
Therefore, the expanded form of (x+10)(x-9) is x² + x - 90.
Why is FOIL important?
The FOIL method helps us to systematically multiply binomials and ensure that we don't miss any terms. It's a simple and efficient way to expand expressions like this one.
Further Applications
The expanded form of (x+10)(x-9) is a quadratic expression. This type of expression can be used in various applications, including:
- Solving quadratic equations: Setting the expression equal to zero and solving for x.
- Graphing parabolas: The expression represents the equation of a parabola, which can be graphed to visualize its shape and intercepts.
- Modeling real-world phenomena: Quadratic expressions can be used to model various phenomena, such as projectile motion or the growth of populations.
By understanding how to expand binomials and work with quadratic expressions, we can gain valuable insights into various mathematical and real-world problems.