To find the greatest common factor (GCF) of the two expressions \(2x^2\) and \(4x^2y\), we start by factoring each expression:
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The first expression \(2x^2\) can be factored as: \[ 2x^2 = 2 \cdot x \cdot x \]
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The second expression \(4x^2y\) can be factored as: \[ 4x^2y = 4 \cdot x \cdot x \cdot y = (2 \cdot 2) \cdot x \cdot x \cdot y \]
Now, we compare the common factors:
- The coefficients are \(2\) (from \(2x^2\)) and \(4\) (from \(4x^2y\)). The GCF of 2 and 4 is \(2\).
- The variable \(x\) appears in both expressions, and the lowest power is \(x^2\).
- The variable \(y\) appears only in \(4x^2y\) and not in \(2x^2\), so it does not contribute to the GCF.
Now we can combine the GCF of the coefficients and the variables: \[ \text{GCF} = 2 \cdot x^2 = 2x^2 \]
Therefore, the greatest common factor of \(2x^2\) and \(4x^2y\) is \(2x^2\).
The answer from your options is: 2x² (which is equivalent to 2x squared).