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!

Learn how to simplify the expression (ax + b)^2 step by step using the distributive property and the FOIL method. This problem covers key algebraic concepts such as binomial expansion, combining like terms, and quadratic expressions. Suitable for students in Grades 8-10.

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