To simplify the expression \( a^2(a + 4) \), you need to distribute \( a^2 \) across each term inside the parentheses.

\[
a^2(a + 4) = a^2 \cdot a + a^2 \cdot 4
\]

Now, multiply:

\[
a^2 \cdot a = a^3
\]
\[
a^2 \cdot 4 = 4a^2
\]

So, the simplified expression is:

\[
a^3 + 4a^2
\]

Would you like more details or have any questions?

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Here are 8 related questions to explore further:

1. How would you factor the expression \( a^3 + 4a^2 \)?
2. What happens if you substitute \( a = 3 \) into the simplified expression?
3. How would you differentiate the expression \( a^3 + 4a^2 \) with respect to \( a \)?
4. What is the degree of the polynomial \( a^3 + 4a^2 \)?
5. How would the expression change if the coefficient \( 4 \) were replaced with another number?
6. Can you factor out \( a^2 \) from the original expression in a different way?
7. What is the sum of the coefficients in the simplified expression?
8. How does the expression \( a^2(a + 4) \) relate to the distributive property?

**Tip:** When multiplying terms, remember that the exponents of like bases are added together.

Learn how to simplify the algebraic expression a^2(a + 4) step-by-step. This problem involves distributing a^2 across the terms inside the parentheses and is suitable for students in Grades 7-9 studying algebraic expressions and the distributive property.

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