7. \( 17 m^{6} n^{11}-\left(5 m^{5} n^{2}\right)\left(4 m h^{9}\right) \)

To factor the expression \( 17 m^{6} n^{11} - (5 m^{5} n^{2})(4 m h^{9}) \), we first compute the second term: \[ (5 m^{5} n^{2})(4 m h^{9}) = 20 m^{6} n^{2} h^{9} \] So, we rewrite the original expression: \[ 17 m^{6} n^{11} - 20 m^{6} n^{2} h^{9} \] Next, observe that both terms share a common factor of \( m^{6} \): \[ m^{6}(17 n^{11} - 20 n^{2} h^{9}) \] Now, the expression can be simplified to \( m^{6}(17 n^{11} - 20 n^{2} h^{9}) \), and the \( n^{2} \) can be factored out from the second term inside the parentheses: \[ m^{6}(n^{2}(17 n^{9} - 20 h^{9})) \] Thus, the fully factored form of the expression is: \[ m^{6} n^{2} (17 n^{9} - 20 h^{9}) \]