To simplify the expression \( 2x(4+x) \), you can use the distributive property:
\[ 2x(4+x) = 2x \cdot 4 + 2x \cdot x \]
Calculating each term:
\[ 2x \cdot 4 = 8x \] \[ 2x \cdot x = 2x^2 \]
Now, combine the terms:
\[ 2x(4+x) = 8x + 2x^2 \]
So, the simplified expression is:
\[ 2x^2 + 8x \]