To use the Distributive Property to multiply the polynomial \( 3x^2 \) with the expression \( (2x^4 - 15x) \), we can distribute \( 3x^2 \) to each term inside the parentheses.
Here are the steps:
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Multiply \( 3x^2 \) by the first term \( 2x^4 \): \[ 3x^2 \cdot 2x^4 = 6x^{2+4} = 6x^6 \]
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Multiply \( 3x^2 \) by the second term \( -15x \): \[ 3x^2 \cdot (-15x) = -45x^{2+1} = -45x^3 \]
Now, combine the results: \[ 3x^2(2x^4 - 15x) = 6x^6 - 45x^3 \]
So, the final answer is: \[ \boxed{6x^6 - 45x^3} \]