## Expanding (u-7)^2: A Step-by-Step Guide

The expression (u-7)^2 represents the square of the binomial (u-7). To expand this, we need to apply the distributive property or the FOIL method.

### Understanding the Basics

**Binomial:**An algebraic expression with two terms, like (u-7).**Square:**Multiplying a number or expression by itself.**FOIL Method:**An acronym for "First, Outer, Inner, Last". It helps multiply binomials systematically.

### Expanding using the FOIL Method

**First:**Multiply the**first**terms of each binomial: u * u = u²**Outer:**Multiply the**outer**terms: u * -7 = -7u**Inner:**Multiply the**inner**terms: -7 * u = -7u**Last:**Multiply the**last**terms: -7 * -7 = 49

Now, combine all the terms:

u² - 7u - 7u + 49

Finally, simplify by combining like terms:

**u² - 14u + 49**

### Expanding using the Distributive Property

- Rewrite (u-7)^2 as (u-7)(u-7)
- Distribute the first term of the first binomial across the second binomial: u(u-7) - 7(u-7)
- Distribute further: u² - 7u - 7u + 49
- Combine like terms:
**u² - 14u + 49**

### Conclusion

Both methods lead to the same expanded form of (u-7)²: **u² - 14u + 49**. This expression is now in a simplified form, allowing for further manipulation or analysis in various mathematical contexts.