To factor the expression \(2a^3b + 6a^2b^2\), we need to find the greatest common factor (GCF) of the two terms.
- Identify the coefficients and their GCF: The coefficients are 2 and 6. The GCF of 2 and 6 is 2.
- Identify the common variables: The terms have \(a^3\) and \(a^2\) in them. The GCF for the \(a\) terms is \(a^2\). For the \(b\) terms, we have \(b\) and \(b^2\), so the GCF is \(b\).
Now we combine these GCFs:
- GCF = \(2a^2b\)
Next, we can factor this out:
\[ 2a^3b + 6a^2b^2 = 2a^2b(a + 3b) \]
Thus, the expression factored out with the GCF is:
\[ 2a^2b(a + 3b) \]
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