use the distributive property to mulitply the polynomials -5t^3(6t^7-9t)

Answer 1

To use the distributive property to multiply the polynomial \(-5t^3\) with the polynomial \((6t^7 - 9t)\), you will distribute \(-5t^3\) to each term inside the parentheses.

Here’s how the multiplication works step by step:

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

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

Now, combine the results: \[ -5t^3(6t^7 - 9t) = -30t^{10} + 45t^{4} \]

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