Factor the following expression. \[ 24 u^{4} v^{3} y^{6}-18 u^{7} v^{5} \]

To factor the expression \( 24 u^{4} v^{3} y^{6} - 18 u^{7} v^{5} \), first identify the greatest common factor (GCF) of the coefficients and the variables. The GCF of the coefficients 24 and 18 is 6. For the variable parts, the GCF is \( u^{4} v^{3} \). Thus, we can factor out \( 6 u^{4} v^{3} \): \[ 6 u^{4} v^{3} (4 y^{6} - 3 u^{3} v^{2}) \] This gives us the fully factored form: \[ 6 u^{4} v^{3} (4 y^{6} - 3 u^{3} v^{2}) \]