(x%2B6).jpeg "(x-6)(x+6)")
Expanding and Simplifying (x-6)(x+6)
The expression (x-6)(x+6) is a product of two binomials. To simplify it, we can use the FOIL method:
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 this to our expression:
F: (x)(x) = x² O: (x)(6) = 6x I: (-6)(x) = -6x L: (-6)(6) = -36
Now, add all the terms together:
x² + 6x - 6x - 36
Notice that the 6x and -6x terms cancel each other out. This leaves us with:
x² - 36
Therefore, the simplified form of (x-6)(x+6) is x² - 36.
Special Case: Difference of Squares
The expression (x-6)(x+6) is a classic example of a difference of squares. This is a pattern that arises when you multiply two binomials where one is the sum of two terms and the other is the difference of the same two terms.
General Pattern: (a + b)(a - b) = a² - b²
In our case, 'a' is 'x' and 'b' is '6'.
Recognizing this pattern allows us to simplify these types of expressions quickly without using the FOIL method.
Key takeaway: Understanding the difference of squares pattern can save you time and effort when simplifying expressions.