Questions: 18v^4w^6-14vw^4x^5

18v^4w^6-14vw^4x^5
Transcript text: $18 v^{4} w^{6}-14 v w^{4} x^{5}$
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Solution

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Solution Steps

Step 1: Identify the Terms

We start with the expression \(18 v^{4} w^{6} - 14 v w^{4} x^{5}\). The two terms are \(18 v^{4} w^{6}\) and \(14 v w^{4} x^{5}\).

Step 2: Find the Greatest Common Factor (GCF)

Next, we determine the GCF of the two terms. The GCF is \(2 v w^{4}\), which is the highest power of each variable that appears in both terms.

Step 3: Factor Out the GCF

We factor the GCF out of the expression: \[ 18 v^{4} w^{6} - 14 v w^{4} x^{5} = 2 v w^{4} \left( \frac{18 v^{4} w^{6}}{2 v w^{4}} - \frac{14 v w^{4} x^{5}}{2 v w^{4}} \right) \] This simplifies to: \[ 2 v w^{4} \left( 9 v^{3} w^{2} - 7 x^{5} \right) \]

Step 4: Write the Final Factored Form

The final factored form of the expression is: \[ 2 v w^{4} \left( 9 v^{3} w^{2} - 7 x^{5} \right) \]

Final Answer

\(\boxed{2 v w^{4} (9 v^{3} w^{2} - 7 x^{5})}\)

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