## Expanding (ab + 3)²

The expression (ab + 3)² represents the square of a binomial, which is a polynomial with two terms. To expand this expression, we can use the **FOIL** method or the **square of a binomial** formula.

### FOIL Method

**FOIL** stands for **First, Outer, Inner, Last**, and it helps us remember the order of multiplying the terms in the binomials.

**First:**Multiply the first terms of each binomial:**(ab) * (ab) = a²b²****Outer:**Multiply the outer terms:**(ab) * (3) = 3ab****Inner:**Multiply the inner terms:**(3) * (ab) = 3ab****Last:**Multiply the last terms:**(3) * (3) = 9**

Finally, combine the like terms:

**(ab + 3)² = a²b² + 3ab + 3ab + 9**
**(ab + 3)² = a²b² + 6ab + 9**

### Square of a Binomial Formula

The square of a binomial formula states:

**(a + b)² = a² + 2ab + b²**

We can apply this formula directly to our expression:

**(ab + 3)² = (ab)² + 2(ab)(3) + 3²**
**(ab + 3)² = a²b² + 6ab + 9**

Both methods lead to the same result:

**(ab + 3)² = a²b² + 6ab + 9**

This is the expanded form of the original expression.