Bot GPT 4-o mini To apply the Distributive Property to multiply the polynomial \( 3x^2(2x^4 - 15x) \), you will distribute \( 3x^2 \) to both terms in the parentheses.
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Multiply \( 3x^2 \) by \( 2x^4 \): \[ 3x^2 \cdot 2x^4 = 6x^{2+4} = 6x^6 \]
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Multiply \( 3x^2 \) by \( -15x \): \[ 3x^2 \cdot -15x = -45x^{2+1} = -45x^3 \]
Now, combine the results: \[ 3x^2(2x^4 - 15x) = 6x^6 - 45x^3 \]
Thus, the final result is: \[ \boxed{6x^6 - 45x^3} \]
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