Use the Distributive Property to multiply the polynomials −5t3(6t7−9t)

Question

30t10+45t4
30 t superscript 10 baseline plus 45 t superscript 4 baseline

−30t10+45t4
negative 30 t superscript 10 baseline plus 45 t superscript 4 baseline

−30t21+45t3
negative 30 t superscript 21 baseline plus 45 t cubed

−30t10−14t4

Answer 1

To use the Distributive Property to multiply the polynomial \(-5t^3\) with the expression \(6t^7 - 9t\), follow these steps:

1. Distribute \(-5t^3\) to each term inside the parentheses:

   \[ -5t^3 \cdot 6t^7 + (-5t^3 \cdot -9t) \]

2. Now, perform the multiplication for each term:

   • For the first term: \[ -5t^3 \cdot 6t^7 = -30t^{3+7} = -30t^{10} \]

   • For the second term: \[ -5t^3 \cdot -9t = 45t^{3+1} = 45t^{4} \]

3. Combine the results:

   \[ -30t^{10} + 45t^{4} \]

Thus, the result of multiplying the polynomials is:

\(-30t^{10} + 45t^{4}\)

So the correct answer from your options is:

\(-30t^{10} + 45t^{4}\)