Use the distributive property to write each of the following products as polynomials. -16t(2t^2-2t+3)

To apply the distributive property to the expression \(-16t(2t^2 - 2t + 3)\), you multiply \(-16t\) by each term inside the parentheses.

Let's go step by step:

\[
-16t(2t^2 - 2t + 3) = (-16t \cdot 2t^2) + (-16t \cdot -2t) + (-16t \cdot 3)
\]

Now perform the multiplication for each term:

1. \(-16t \cdot 2t^2 = -32t^3\)
2. \(-16t \cdot -2t = 32t^2\)
3. \(-16t \cdot 3 = -48t\)

Thus, the polynomial is:

\[
-32t^3 + 32t^2 - 48t
\]

Would you like more details or have any questions? Here are some related questions to further your understanding:

1. How does the distributive property work for binomials or trinomials?
2. Can you simplify \(-16t(2t^2 - 2t + 3)\) using another method?
3. What is the degree of the polynomial \(-32t^3 + 32t^2 - 48t\)?
4. How would you factor out common terms from a polynomial like this one?
5. How do you apply the distributive property when exponents are involved?

**Tip**: Always distribute to every term inside the parentheses to ensure correct expansion.

Learn how to apply the distributive property to expand the expression -16t(2t^2 - 2t + 3) into the polynomial -32t^3 + 32t^2 - 48t. This problem introduces key algebraic concepts like polynomial expansion using the distributive property. Suitable for students in Grades 8-10.

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