Fully simplify \( 4 x y+3 x+6+2 y x+x+y \)

To simplify the expression \( 4xy + 3x + 6 + 2yx + x + y \), we start by combining like terms. 1. Notice that \( 2yx \) is the same as \( 2xy \). 2. Therefore, we can rewrite the expression as \( 4xy + 2xy + 3x + x + 6 + y \). 3. Now combine the \( xy \) terms: \( 4xy + 2xy = 6xy \). 4. Next, combine the \( x \) terms: \( 3x + x = 4x \). 5. The \( 6 \) and \( y \) remain as they are. Putting it all together, we have: \[ 6xy + 4x + y + 6 \] Thus, the fully simplified expression is: \[ 6xy + 4x + y + 6 \]