## Understanding (x-12)^2

(x-12)^2 is a mathematical expression that represents the **square of the difference between x and 12**. In simpler terms, it means multiplying the quantity (x-12) by itself.

Here's a breakdown:

**1. Parentheses First:**

- The parentheses indicate that we must perform the operation within them first. In this case, we subtract 12 from x.

**2. Squaring:**

- The exponent 2 means we multiply the result of (x-12) by itself.

**Expanding the Expression**

We can expand (x-12)^2 using the **FOIL** method (First, Outer, Inner, Last):

**First:**x * x = x^2**Outer:**x * -12 = -12x**Inner:**-12 * x = -12x**Last:**-12 * -12 = 144

Combining the terms, we get:

**(x-12)^2 = x^2 - 12x - 12x + 144**

**Simplifying the Expression:**

Combining the like terms, we get the simplified form:

**(x-12)^2 = x^2 - 24x + 144**

**Applications**

This expression is widely used in various mathematical and scientific applications, including:

**Algebra:**Solving quadratic equations and simplifying expressions.**Calculus:**Finding derivatives and integrals.**Physics:**Modelling motion and analyzing forces.**Geometry:**Calculating areas and volumes.

**Key Points**

**Parentheses matter:**Remember to perform the operation inside the parentheses first.**FOIL method:**This method helps to expand squared expressions.**Simplified form:**The simplified form of (x-12)^2 is x^2 - 24x + 144.

By understanding the concept of squaring and expanding expressions, you can effectively work with (x-12)^2 and its various applications.