## Understanding the Standard Form of (x+3)(x-3)

In algebra, the standard form of a quadratic equation is **ax² + bx + c**, where a, b, and c are constants. To understand the standard form of (x+3)(x-3), we need to expand the expression using the distributive property or the FOIL method.

### Expanding (x+3)(x-3)

**1. Using the Distributive Property:**

- We distribute each term in the first set of parentheses to the second set of parentheses:
- x(x-3) + 3(x-3)

- Then, we simplify by multiplying:
- x² - 3x + 3x - 9

**2. Using the FOIL Method:**

- FOIL stands for
**First**,**Outer**,**Inner**,**Last**. We multiply each pair of terms as follows:**First:**x * x = x²**Outer:**x * -3 = -3x**Inner:**3 * x = 3x**Last:**3 * -3 = -9

- We then combine the like terms:
- x² - 3x + 3x - 9

### The Standard Form

After simplifying, we get:
**x² - 9**

This is the standard form of the quadratic expression (x+3)(x-3). Notice that the **b** term (the coefficient of x) is 0 in this case.

### Significance of the Standard Form

The standard form of a quadratic expression is crucial because it:

**Simplifies the expression:**It provides a concise and organized way to represent the equation.**Facilitates calculations:**It allows us to easily identify the coefficients (a, b, and c) which are necessary for solving the equation or finding its vertex.**Enables comparisons:**It allows us to compare different quadratic expressions and identify their key features.

In the case of (x+3)(x-3), the standard form x² - 9 reveals that the expression represents a parabola with a vertex at (0, -9) and symmetric about the y-axis. This knowledge helps us understand the graph of the equation and its properties.