To find the greatest common factor (GCF) of the expressions \(2x^2\) and \(4x^2y\), we need to consider the coefficients and the variable parts separately.
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Coefficients:
- The coefficients are 2 and 4.
- The GCF of 2 and 4 is 2.
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Variable parts:
- For \(x^2\), it appears in both expressions, so we take \(x^2\).
- For \(y\), it only appears in \(4x^2y\), so we do not include \(y\) in the GCF.
Now, we multiply the GCF of the coefficients by the GCF of the variable parts:
\[ \text{GCF} = 2 \cdot x^2 = 2x^2 \]
Therefore, the greatest common factor of \(2x^2\) and \(4x^2y\) is \(2x^2\).