(x-8).jpeg "(x+3)(x-8)")
Expanding the Expression (x+3)(x-8)
This expression represents the multiplication of two binomials: (x+3) and (x-8). To expand it, 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 * -8 = -8x
- Inner: Multiply the inner terms of the binomials: 3 * x = 3x
- Last: Multiply the last terms of each binomial: 3 * -8 = -24
Now, add all the results together:
x² - 8x + 3x - 24
Finally, combine the like terms:
x² - 5x - 24
Therefore, the expanded form of (x+3)(x-8) is x² - 5x - 24.
Understanding the Result
This expanded expression represents a quadratic equation, which is a polynomial with the highest power of the variable being 2. The expression can be used to represent various scenarios, such as:
- Area of a rectangle: If (x+3) and (x-8) represent the length and width of a rectangle, the expression represents the area of the rectangle.
- Modeling physical phenomena: Quadratic equations are used in physics to model the motion of projectiles and other physical phenomena.
- Solving for unknown values: The expression can be used to find the roots (solutions) of the equation x² - 5x - 24 = 0, which are the values of x that make the expression equal to zero.
Conclusion
The expansion of (x+3)(x-8) is a fundamental step in understanding and working with quadratic equations. By applying the FOIL method, we can easily expand the expression and gain insights into its various applications.