To simplify $(ax + b)^2$, follow these steps using the distributive property (also known as the FOIL method for binomials):

$(ax + b)^2 = (ax + b)(ax + b)$

Now, apply the distributive property:

1. Multiply the first terms: $(ax) \cdot (ax) = a^2x^2$
2. Multiply the outer terms: $(ax) \cdot b = abx$
3. Multiply the inner terms: $b \cdot (ax) = abx$
4. Multiply the last terms: $b \cdot b = b^2$

Now, combine like terms:

$a^2x^2 + abx + abx + b^2 = a^2x^2 + 2abx + b^2$

So, the simplified expression is:

$(ax + b)^2 = a^2x^2 + 2abx + b^2$

Would you like more details on any of the steps?

Related Questions:

1. How do you apply the distributive property to other binomials?
2. What happens when $a = 1$ in the expression $(ax + b)^2$?
3. How do you simplify higher powers of binomials, such as $(ax + b)^3$?
4. Can you apply this method to expressions like $(x + b)^2$ with more terms?
5. How can you use this result in solving quadratic equations?

Tip: Remember that squaring a binomial always results in three terms if simplified correctly: a square term, a middle term, and a constant term!