## Understanding (x+10)(x-10)

The expression (x+10)(x-10) represents a product of two binomials. This type of multiplication is commonly referred to as "**FOIL**", which stands for **First, Outer, Inner, Last**.

### Expanding the Expression

Let's apply the FOIL method to expand the expression:

**First:**Multiply the first terms of each binomial: (x)(x) = x²**Outer:**Multiply the outer terms: (x)(-10) = -10x**Inner:**Multiply the inner terms: (10)(x) = 10x**Last:**Multiply the last terms: (10)(-10) = -100

Now, combining the terms, we have:

x² - 10x + 10x - 100

Simplifying the expression, we get:

**x² - 100**

### Recognizing a Special Pattern

The expression (x+10)(x-10) is a specific example of a **difference of squares**. This pattern applies when we have two binomials where the only difference is the sign between the terms.

**General Pattern:** (a + b)(a - b) = a² - b²

In our example, a = x and b = 10. Therefore, the expanded form (x² - 100) is the difference of squares.

### Applications

Understanding the difference of squares pattern is useful for:

**Factoring expressions:**You can quickly factor an expression like x² - 100 by recognizing it as a difference of squares.**Solving equations:**If you have an equation like x² - 100 = 0, you can easily factor it into (x + 10)(x - 10) = 0, making it easier to solve.**Simplifying algebraic expressions:**By recognizing the difference of squares pattern, you can simplify complex expressions involving these types of products.

In conclusion, the expression (x+10)(x-10) expands to x² - 100, which is a classic example of the difference of squares pattern. Understanding this pattern is crucial for efficient algebraic manipulation and problem-solving.