Question
Factor the following expression. \[ 24 u^{4} v^{3} y^{6}-18 u^{7} v^{5} \]
Ask by Little Bradley. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factored form is \(6u^{4}v^{3}(4y^{6}-3u^{3}v^{2})\).
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The Deep Dive
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: \[ 6 u^{4} v^{3} (4 y^{6} - 3 u^{3} v^{2}) \]
