To use the distributive property to multiply the polynomial \(-5t^3\) by each term in the polynomial \(6t^7 - 9t\), you will perform the following steps:
- Distribute \(-5t^3\) to \(6t^7\).
- Distribute \(-5t^3\) to \(-9t\).
Let's do the calculations:
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Multiply \(-5t^3\) by \(6t^7\): \[ -5t^3 \cdot 6t^7 = -30t^{3+7} = -30t^{10} \]
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Multiply \(-5t^3\) by \(-9t\): \[ -5t^3 \cdot (-9t) = 45t^{3+1} = 45t^{4} \]
Now, combine both results: \[ -30t^{10} + 45t^{4} \]
Therefore, the final result of multiplying \(-5t^3\) by \(6t^7 - 9t\) is: \[ -30t^{10} + 45t^{4} \]
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