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To expand the given expression \( y^2(8y + 3) \), follow these steps:

1. Distribute \( y^2 \) to both terms inside the parentheses:

\[
y^2(8y + 3) = y^2 \cdot 8y + y^2 \cdot 3
\]

2. Perform the multiplication for each term:
   - \( y^2 \cdot 8y = 8y^3 \) (since \( y^2 \cdot y = y^3 \))
   - \( y^2 \cdot 3 = 3y^2 \)

So, the expanded form is:

\[
8y^3 + 3y^2
\]

Would you like any more details or clarification?

Here are five related questions to further explore the concept:

1. How would you factor the expression \( 8y^3 + 3y^2 \)?
2. What happens if you expand \( y^3(2y^2 + 5) \)?
3. Can you explain the difference between expanding and factoring expressions?
4. How would the expansion change if the expression was \( y^2(8y^2 + 3y) \)?
5. What are the rules for multiplying powers of the same base (like \( y^2 \cdot y^3 \))?

**Tip:** When expanding expressions, always distribute each term outside the parentheses to every term inside the parentheses!

Learn how to expand the polynomial expression y^2(8y + 3) with a detailed, step-by-step solution. This problem covers key algebraic concepts such as polynomial expansion and the distributive law. Suitable for students in Grades 7-9.

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