(u-4)^2

Jasonbradley

3 min read

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Jun 16, 2024

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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

1. Expand the square: u² - 8u + 16 = 25
2. Rearrange: u² - 8u - 9 = 0
3. Factor: (u-9)(u+1) = 0
4. 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.