To expand the expression \((6x + b)(6x + b)\), we can use the distributive property (also known as FOIL for binomials).

\[
(6x + b)(6x + b) = (6x)^2 + 2(6x)(b) + b^2
\]

Now, let's break it down step by step:

1. \((6x)(6x) = 36x^2\)
2. \((6x)(b) = 6xb\), and since there are two of these, we get \(2(6xb) = 12xb\)
3. \((b)(b) = b^2\)

So, the expanded form is:

\[
36x^2 + 12xb + b^2
\]

Would you like more details on any part of this?

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Here are 5 related questions to expand your understanding:

1. How do you apply the distributive property (FOIL) to more complex binomials?
2. What happens when the variables or constants are negative?
3. Can you factor back a trinomial like this one?
4. How would you graph the expression \(36x^2 + 12xb + b^2\)?
5. How do you identify the vertex of a quadratic expression?

**Tip:** When expanding binomials, always check if the middle terms can be combined to simplify further!

Explore how to expand the binomial (6x + b)(6x + b) step-by-step using the distributive property (FOIL). This lesson breaks down each component, covering key algebraic concepts like binomial expansion and quadratic expressions. Perfect for students in Grades 8-10.

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