Use the Distributive Property to multiply the following polynomials: 3x2(2x4−15x)

Question

.(1 point)
3x2(2x4−15x)=

Answer 1

To apply the Distributive Property to multiply the polynomial \(3x^2(2x^4 - 15x)\), we'll distribute \(3x^2\) to each term inside the parentheses.

1. Multiply \(3x^2\) by \(2x^4\):

\[ 3x^2 \cdot 2x^4 = 6x^{2+4} = 6x^6 \]

2. Multiply \(3x^2\) by \(-15x\):

\[ 3x^2 \cdot (-15x) = -45x^{2+1} = -45x^3 \]

Now, combine these results:

\[ 3x^2(2x^4 - 15x) = 6x^6 - 45x^3 \]

So the final answer is:

\[ \boxed{6x^6 - 45x^3} \]