(x-6)(x+6) Simplify

2 min read Jun 17, 2024

Simplifying (x-6)(x+6)

In mathematics, simplifying expressions is a fundamental skill. One common type of expression that requires simplification involves multiplying binomials, such as (x-6)(x+6).

Understanding the Concept

This expression represents the product of two binomials. To simplify it, we can utilize 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.

Applying the FOIL Method

Let's apply the FOIL method to our expression:

First: (x) * (x) = x²
Outer: (x) * (6) = 6x
Inner: (-6) * (x) = -6x
Last: (-6) * (6) = -36

Combining Like Terms

Now, we have the following terms: x² + 6x - 6x - 36. Notice that the terms 6x and -6x are like terms, meaning they have the same variable and exponent. We can combine them:

x² + 6x - 6x - 36 = x² - 36

Final Result

Therefore, the simplified form of (x-6)(x+6) is x² - 36.

Key Observation

This simplification demonstrates a pattern known as the difference of squares. The expression (x-6)(x+6) is a special case where the binomials differ only in their signs. In general, the difference of squares pattern can be expressed as:

(a-b)(a+b) = a² - b²

This pattern is a useful shortcut for simplifying expressions with this specific form.