Final answer:
The product of (x+8)(x-1) is found using the FOIL method, resulting in x² + 7x - 8. This exercise demonstrates the broader concept of Multiplication of Exponentials, where like terms are combined and signs determined by multiplication rules.
Step-by-step explanation:
When asked to find the product of (x+8)(x-1), we use the FOIL method to multiply two binomials. This stands for First, Outer, Inner, Last, referring to the terms within each parenthesis. Here's how it works:
- First: Multiply the first terms in each parentheses (x*x = x²).
- Outer: Multiply the outer terms (x*(-1) = -x).
- Inner: Multiply the inner terms (8*x = 8x).
- Last: Multiply the last terms (8*(-1) = -8).
Now, combine these results to get:
x² - x + 8x - 8
Combine like terms (in this case, the -x and the 8x):
x² + 7x - 8 is the final product.
This is an example of Multiplication of Exponentials, as we also see in expressions where we need to add exponents of exponential terms.
Note also that when multiplying binomials, the resulting sign of each term follows the rules of multiplication, such as when two positive numbers multiply or when a positive and a negative number multiply, affecting the sign of the result.