https://file.aiquickdraw.com/mathbot/file/1725895397748t89vfpdy.jpg

The expression shown in the image is:

\[
(3x + 1)(3x + 1)
\]

This is a multiplication of two binomials. It can be expanded using the distributive property (also known as the FOIL method for binomials).

Let's go through the steps:

1. Multiply the first terms: \( 3x \cdot 3x = 9x^2 \)
2. Multiply the outer terms: \( 3x \cdot 1 = 3x \)
3. Multiply the inner terms: \( 1 \cdot 3x = 3x \)
4. Multiply the last terms: \( 1 \cdot 1 = 1 \)

Now, combine like terms:

\[
9x^2 + 3x + 3x + 1 = 9x^2 + 6x + 1
\]

So the expanded form of the expression is:

\[
9x^2 + 6x + 1
\]

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. What is the FOIL method and how does it apply to binomial expansion?
2. How do you simplify expressions after expanding binomials?
3. Can you factor the expression \(9x^2 + 6x + 1\) back into binomials?
4. How does the distributive property work in polynomial multiplication?
5. What other techniques are useful when multiplying polynomials?

**Tip:** When multiplying binomials, always look for opportunities to combine like terms to simplify your final expression.

Learn how to expand and simplify the binomial expression (3x + 1)(3x + 1) using the distributive property. This problem covers key algebraic concepts like binomial expansion and quadratic expressions, suitable for students in Grades 8-10.

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