## Expanding (a + 3b)^2

The expression (a + 3b)^2 represents the square of the binomial (a + 3b). To expand this expression, we can use the **FOIL** method or the **square of a binomial** formula.

### Using FOIL Method

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

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

Now, add all the terms together:

a^2 + 3ab + 3ab + 9b^2

Finally, combine the like terms:

**a^2 + 6ab + 9b^2**

### Using Square of a Binomial Formula

The square of a binomial formula states:

**(a + b)^2 = a^2 + 2ab + b^2**

In our case, a = a and b = 3b. Substituting these values into the formula:

(a + 3b)^2 = a^2 + 2(a)(3b) + (3b)^2

Simplifying:

**a^2 + 6ab + 9b^2**

### Conclusion

Both methods lead to the same answer: **(a + 3b)^2 = a^2 + 6ab + 9b^2**. Understanding these methods allows you to expand similar expressions easily and efficiently.