Question

Use the Distributive Property to multiply the polynomials −5t3(6t7−9t).(1 point)%0D%0AResponses%0D%0A%0D%0A−30t21+45t3%0D%0Anegative 30 t superscript 21 baseline plus 45 t cubed%0D%0A%0D%0A30t10+45t4%0D%0A30 t superscript 10 baseline plus 45 t superscript 4 baseline%0D%0A%0D%0A−30t10+45t4%0D%0Anegative 30 t superscript 10 baseline plus 45 t superscript 4 baseline%0D%0A%0D%0A−30t10−14t4

Answer 1

To multiply the polynomial \(-5t^3(6t^7 - 9t)\) using the Distributive Property, we apply the distributive rule, which states that \(a(b + c) = ab + ac\).

Let's distribute \(-5t^3\) to each term inside the parentheses:

1. **Multiply \(-5t^3\) by \(6t^7\):**
\[
-5t^3 \cdot 6t^7 = -30t^{3+7} = -30t^{10}
\]

2. **Multiply \(-5t^3\) by \(-9t\):**
\[
-5t^3 \cdot -9t = 45t^{3+1} = 45t^4
\]

Now combine these results:
\[
-30t^{10} + 45t^4
\]

So the final answer, using the Distributive Property, is:
\[
\boxed{-30t^{10} + 45t^4}
\]