Fully simplify \( 2 k n+3 n r+8 n k+5 k r+6 r n \)

To simplify the expression \( 2 k n + 3 n r + 8 n k + 5 k r + 6 r n \), we first look for like terms. Notice that \( 2 k n \) and \( 8 n k \) are similar terms, as \( k n \) and \( n k \) are the same when multiplied. First, combine \( 2 k n \) and \( 8 n k \): \[ 2 k n + 8 n k = 10 k n. \] Next, we group \( 3 n r \), \( 6 r n \), and \( 5 k r \): The terms \( 3 n r \) and \( 6 r n \) can also be combined since \( r n \) and \( n r \) are the same: \[ 3 n r + 6 r n = 9 n r. \] Now we rewrite the entire expression: \[ 10 k n + 9 n r + 5 k r. \] So, the fully simplified form of the expression is \( 10 k n + 9 n r + 5 k r \).