Use the Distributive Property to multiply the following polynomials: 3x^2(2x^4−15x) .(1 point) 3x^2(2x^4−15x)

Answer 1

To multiply the polynomial \(3x^2(2x^4 - 15x)\) using the Distributive Property, distribute \(3x^2\) to each term inside the parentheses:

\[ 3x^2 \cdot 2x^4 + 3x^2 \cdot (-15x) \]

Calculating each term:

1. For the first term: \[ 3x^2 \cdot 2x^4 = 6x^{2+4} = 6x^6 \]

2. For the second term: \[ 3x^2 \cdot (-15x) = -45x^{2+1} = -45x^3 \]

Now, combine the results:

\[ 6x^6 - 45x^3 \]

So, the final result of multiplying \(3x^2(2x^4 - 15x)\) is:

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