To factor out the greatest common factor (GCF) from the expression \(24ab^2c + 18a^3b\), we first need to determine the GCF of the coefficients and the variables in each term.
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Coefficients: The coefficients are \(24\) and \(18\).
- The GCF of \(24\) and \(18\) is \(6\).
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Variables:
- For \(a\): The minimum power of \(a\) present in both terms is \(a^1\) (from \(24ab^2c\)).
- For \(b\): The minimum power of \(b\) present in both terms is \(b^1\) (from \(18a^3b\)).
- For \(c\): \(c\) is only present in the first term, so we do not include it in the GCF.
Putting all of this together, the GCF is \(6ab\).
Now, we can factor out \(6ab\) from the original expression:
\[ 24ab^2c + 18a^3b = 6ab(4bc + 3a^2) \]
Thus, the expression \(24ab^2c + 18a^3b\) factored out by the GCF is:
\[ 6ab(4bc + 3a^2) \]
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