Questions: Real Numbers and Linear Equations Distributive property: Integer coefficients Use the distributive property to remove the parentheses -6(-v^3+1-2x^2)

Solution Steps

We start with the expression given in the problem, which is

\[ -6\left(-v^{3}+1-2 x^{2}\right). \]

Using the distributive property, we distribute \(-6\) across each term inside the parentheses:

\[ -6 \cdot (-v^{3}) + -6 \cdot 1 + -6 \cdot (-2x^{2}). \]

Now, we simplify each term:

\[ 6v^{3} + 6 - 12x^{2}. \]

Rearranging the terms gives us the final expanded expression:

\[ 6v^{3} + 12x^{2} - 6. \]

Final Answer