Question

Use the Distributive Property to multiply the polynomials −5t3(6t7−9t) .(1 point) Responses −30t10+45t4 negative 30 t superscript 10 baseline plus 45 t superscript 4 baseline −30t10−14t4 negative 30 t superscript 10 baseline minus 14 t superscript 4 baseline −30t21+45t3 negative 30 t superscript 21 baseline plus 45 t cubed 30t10+45t4

Answer 1

To use the Distributive Property to multiply the polynomial \(-5t^3(6t^7 - 9t)\), we'll 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, we can combine these results:

\[ -5t^3(6t^7 - 9t) = -30t^{10} + 45t^4 \]

Thus, the final answer is:

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

Therefore, the correct response is −30t10+45t4.