Expand (sqrt(x) + 3x)*4 + (sqrt(x) - 3x)*4.

Answer 1

To expand the expression \((\sqrt{x} + 3x) \cdot 4 + (\sqrt{x} - 3x) \cdot 4\), we can start by distributing the \(4\) in both terms.

1. Distributing \(4\) in the first term:

\[ (\sqrt{x} + 3x) \cdot 4 = 4\sqrt{x} + 12x \]

2. Distributing \(4\) in the second term:

\[ (\sqrt{x} - 3x) \cdot 4 = 4\sqrt{x} - 12x \]

Now, we can combine the expanded results:

\[ (4\sqrt{x} + 12x) + (4\sqrt{x} - 12x) \]

Now, combining like terms:

1. For \(\sqrt{x}\):

\[ 4\sqrt{x} + 4\sqrt{x} = 8\sqrt{x} \]

2. For \(x\):

\[ 12x - 12x = 0 \]

Putting it all together:

\[ 8\sqrt{x} + 0 = 8\sqrt{x} \]

Thus, the final expanded expression is:

\[ \boxed{8\sqrt{x}} \]