## Expanding (x+3)(x-3) into Standard Form

The expression (x+3)(x-3) represents the product of two binomials. To express it in standard form, we need to expand the product and simplify it.

### Using the FOIL Method

The FOIL method is a common technique for multiplying binomials. It stands for **F**irst, **O**uter, **I**nner, **L**ast, which represent the terms we multiply:

**First:**Multiply the first terms of each binomial: x * x = x²**Outer:**Multiply the outer terms of the binomials: x * -3 = -3x**Inner:**Multiply the inner terms of the binomials: 3 * x = 3x**Last:**Multiply the last terms of each binomial: 3 * -3 = -9

Now, we combine the terms: x² - 3x + 3x - 9

Notice that the -3x and 3x terms cancel each other out. This leaves us with:

**x² - 9**

### Understanding the Pattern

The expression (x+3)(x-3) is a special case of the **difference of squares** pattern:

(a + b)(a - b) = a² - b²

In our case, a = x and b = 3. This pattern is useful to recognize because it allows us to quickly expand expressions of this form.

### Standard Form

The final expression, **x² - 9**, is in standard form. It is a quadratic polynomial with the highest power of x being 2, followed by a constant term.

**In summary, (x+3)(x-3) expands to x² - 9 in standard form. This demonstrates the difference of squares pattern, which can be used to simplify similar expressions.**