(x-6)(x+6)

2 min read Jun 17, 2024
(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) = 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.

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