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