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We are given the expression:

\[
-4w(w^2 - 9)
\]

To simplify this expression into a polynomial in standard form, we apply the distributive property by multiplying \(-4w\) with each term inside the parentheses:

\[
-4w(w^2 - 9) = -4w \cdot w^2 + (-4w \cdot -9)
\]

Now simplify each term:

\[
-4w \cdot w^2 = -4w^3
\]
\[
-4w \cdot (-9) = +36w
\]

Thus, the simplified polynomial is:

\[
-4w^3 + 36w
\]

The polynomial in standard form is:

\[
-4w^3 + 36w
\]

Would you like further details or explanations?

Here are 5 related questions to expand on this:

1. How do you factor polynomials like the one above?
2. What is the degree of a polynomial, and how is it determined?
3. Can polynomials have negative exponents or fractions as powers?
4. How would you solve the equation if it were set equal to zero?
5. What are some real-life applications of polynomials?

**Tip**: Always check if terms can be factored further after simplification to ensure you have the most reduced form of the polynomial!

Learn how to simplify the polynomial expression -4w(w^2 - 9) using the distributive property. This problem involves applying algebraic concepts such as multiplying terms and arranging the result in standard form. Suitable for students in Grades 8-10.

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