## Understanding (u-4)^2

The expression (u-4)^2 represents the square of the binomial (u-4). Let's break down how to simplify and work with this expression.

### Expanding the Expression

To expand (u-4)^2, we can use the FOIL method (First, Outer, Inner, Last):

**First:**u * u = u²**Outer:**u * -4 = -4u**Inner:**-4 * u = -4u**Last:**-4 * -4 = 16

Adding these terms together gives us:

**(u - 4)^2 = u² - 4u - 4u + 16**

Simplifying the expression, we get:

**(u - 4)^2 = u² - 8u + 16**

### Key Points to Remember:

**Squaring a binomial:**Remember that (u-4)^2 is NOT the same as u² - 4². You need to expand the binomial using the FOIL method or by recognizing the pattern of squaring a difference: (a-b)² = a² - 2ab + b².**Factoring:**The expression u² - 8u + 16 can be factored back into (u-4)².**Applications:**This expression is common in algebra and calculus, and understanding its expansion is crucial for solving equations and working with functions.

### Example:

Let's say we need to solve the equation:

**(u-4)² = 25**

**Expand the square:**u² - 8u + 16 = 25**Rearrange:**u² - 8u - 9 = 0**Factor:**(u-9)(u+1) = 0**Solve for u:**u = 9 or u = -1

Therefore, the solutions to the equation (u-4)² = 25 are u = 9 and u = -1.

By understanding the expansion and manipulation of (u-4)², you'll be able to confidently work with it in various mathematical contexts.