## Expanding (y-4)^2

The expression (y-4)^2 represents the square of the binomial (y-4). To expand it, we can use the **FOIL method** or the **square of a binomial pattern**.

### Using the FOIL Method

**FOIL** stands for **First, Outer, Inner, Last**. This method helps us multiply two binomials together:

**First:**Multiply the**first**terms of each binomial:**y * y = y^2****Outer:**Multiply the**outer**terms:**y * -4 = -4y****Inner:**Multiply the**inner**terms:**-4 * y = -4y****Last:**Multiply the**last**terms:**-4 * -4 = 16**

Now, combine the terms: **y^2 - 4y - 4y + 16**

Finally, simplify by combining like terms: **y^2 - 8y + 16**

### Using the Square of a Binomial Pattern

The square of a binomial pattern states that: **(a - b)^2 = a^2 - 2ab + b^2**

In our case, a = y and b = 4. Applying the pattern, we get:

**y^2 - 2(y)(4) + 4^2**

Simplifying, we obtain: **y^2 - 8y + 16**

### Conclusion

Both methods lead to the same result: **(y-4)^2 = y^2 - 8y + 16**. Expanding a squared binomial is a fundamental skill in algebra, particularly useful for solving equations and simplifying expressions.