Use the Distributive Property to multiply the polynomials −5t3(6t7−9t) .(1 point)

Question

Responses

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

−30t10−14t4
negative 30 t superscript 10 baseline minus 14 t superscript 4 baseline

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

−30t10+45t4

Answer 1

To use the Distributive Property to multiply the polynomial \(-5t^3(6t^7 - 9t)\), we will distribute \(-5t^3\) to both terms in 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 the results from both multiplications: \[ -30t^{10} + 45t^{4} \]

So the final result is: \[ -30t^{10} + 45t^{4} \]

This matches the response: −30t10 + 45t4 (negative 30 t superscript 10 baseline plus 45 t superscript 4 baseline).