## Simplifying (y+3)^2

The expression (y+3)^2 represents the square of the binomial (y+3). To simplify this, we can apply the **FOIL method** or the **square of a binomial pattern**.

### FOIL Method

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

**First:**Multiply the first terms of each binomial:**y * y = y^2****Outer:**Multiply the outer terms of the binomials:**y * 3 = 3y****Inner:**Multiply the inner terms of the binomials:**3 * y = 3y****Last:**Multiply the last terms of each binomial:**3 * 3 = 9**

Now, we add all the terms together: **y^2 + 3y + 3y + 9**

Finally, we combine the like terms: **y^2 + 6y + 9**

Therefore, (y+3)^2 simplified is **y^2 + 6y + 9**

### Square of a Binomial Pattern

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

Applying this pattern to our expression:

**a = y****b = 3**

Substituting these values in the pattern: **y^2 + 2(y)(3) + 3^2**

Simplifying this expression gives us: **y^2 + 6y + 9**

This method provides a quicker way to simplify the expression.

### Conclusion

Both the FOIL method and the square of a binomial pattern lead to the same simplified expression: **y^2 + 6y + 9**. Choose the method you find easiest and most comfortable to apply.