Factor the following expression. \( 18 u^{9} x^{8}-24 u^{3} x^{4} y^{5} \)

To factor the expression \( 18 u^{9} x^{8} - 24 u^{3} x^{4} y^{5} \), follow these steps: 1. **Identify the Greatest Common Factor (GCF) for the coefficients:** - The coefficients are 18 and 24. - The GCF of 18 and 24 is **6**. 2. **Identify the GCF for each variable:** - For \( u \): The smallest exponent is \( u^3 \). - For \( x \): The smallest exponent is \( x^4 \). - The variable \( y \) only appears in the second term, so it doesn't contribute to the GCF. 3. **Factor out the GCF from each term:** - **First Term:** \( 18 u^{9} x^{8} \div 6 u^{3} x^{4} = 3 u^{6} x^{4} \) - **Second Term:** \( 24 u^{3} x^{4} y^{5} \div 6 u^{3} x^{4} = 4 y^{5} \) 4. **Write the factored expression:** \[ 6 u^{3} x^{4} \left( 3 u^{6} x^{4} - 4 y^{5} \right) \] **Final Factored Form:** \[ 6u^{3}x^{4}(3u^{6}x^{4} - 4y^{5}) \] Answer: \(6u^{3}x^{4}(3u^{6}x^{4} - 4y^{5})\)