(x%2B8).jpeg "(x-5)(x+8)")
Expanding the Expression (x-5)(x+8)
This expression represents the product of two binomials: (x-5) and (x+8). To expand it, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last, and it helps us systematically multiply each term in the first binomial by each term in the second binomial.
Here's how it works:
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First: Multiply the first terms of each binomial:
x * x = x² -
Outer: Multiply the outer terms of each binomial: x * 8 = 8x
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Inner: Multiply the inner terms of each binomial: -5 * x = -5x
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Last: Multiply the last terms of each binomial: -5 * 8 = -40
Now, we have the expanded terms: x² + 8x - 5x - 40
Finally, combine the like terms: x² + 3x - 40
Therefore, the expanded form of (x-5)(x+8) is x² + 3x - 40.
Understanding the Result
The expanded expression represents a quadratic equation. This means it can be graphed as a parabola. The expression tells us:
- x²: The parabola will open upwards, as the coefficient of x² is positive.
- 3x: This term determines the slope of the parabola.
- -40: This term indicates the y-intercept of the parabola.
By understanding the expansion, we can gain insights into the shape and behavior of the function represented by the expression.