## Expanding (y-1)^2

The expression **(y-1)^2** represents the square of the binomial (y-1). To expand it, we can use the following methods:

### Method 1: Using the FOIL method

FOIL stands for **First, Outer, Inner, Last**. This method helps us multiply two binomials by systematically multiplying each term of the first binomial with each term of the second binomial.

**First:**Multiply the first terms of each binomial: y * y =**y^2****Outer:**Multiply the outer terms of the binomials: y * -1 =**-y****Inner:**Multiply the inner terms of the binomials: -1 * y =**-y****Last:**Multiply the last terms of each binomial: -1 * -1 =**1**

Now, add all the terms together: y^2 - y - y + 1 = **y^2 - 2y + 1**

### Method 2: Using the pattern (a-b)^2 = a^2 - 2ab + b^2

This formula directly applies to our expression, where a = y and b = 1.

Substituting the values: y^2 - 2(y)(1) + 1^2 = **y^2 - 2y + 1**

### Conclusion

Both methods lead to the same expanded form of **(y-1)^2**, which is **y^2 - 2y + 1**. It's important to remember these methods and practice applying them to various binomial expressions.