(x%2B8).jpeg "(x-8)(x+8)")
Expanding the Expression (x-8)(x+8)
This expression represents the product of two binomials: (x-8) and (x+8). To expand it, we can use the FOIL method, which stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Let's apply FOIL to our expression:
F: x * x = x² O: x * 8 = 8x I: -8 * x = -8x L: -8 * 8 = -64
Now, combine the terms: x² + 8x - 8x - 64
Notice that the middle terms, +8x and -8x, cancel each other out. This leaves us with:
x² - 64
This is the expanded form of (x-8)(x+8).
Key Observation:
The expression (x-8)(x+8) is a special case known as the difference of squares. This pattern is evident in the result:
- x² is the square of the first term (x).
- 64 is the square of the second term (8).
- The expression is a difference (subtraction) between these squares.
The general form of the difference of squares is:
(a - b)(a + b) = a² - b²
This pattern is very useful for factoring and simplifying expressions.