Use the box method to distribute and simplify (x+3)(6x^2^−x). Drag and drop the terms to the correct locations of the table.left bracket

1 answer

\[ \begin{array}{|c|c|}
\hline
x & 3 \\
\hline
6x^2 & \\
\hline
-x & \\
\hline
\end{array} \]

First, distribute the \(x\) and \(3\) into the terms in the second row:

\[ \begin{array}{|c|c|}
\hline
x(6x^2) & 3(6x^2) \\
\hline
- x & -3x \\
\hline
\end{array} \]

Now, combine the like terms in the last row:

\[ \begin{array}{|c|c|}
\hline
6x^3 & 18x^2 \\
\hline
- x & -3x \\
\hline
\end{array} \]

Finally, add the terms in the second column:

\[ 6x^3 + 18x^2 - x - 3x = 6x^3 + 18x^2 - 4x \]

So, after distributing and simplifying, \((x+3)(6x^2-x)\) equals \(6x^3 + 18x^2 - 4x\).