Question

What is the greatest common factor of 2x2
and 4x2y
?(1 point)
Responses

4x2
4 x squared

2x2
2 x squared

2x2y
2 x squared y

2xy

Answer 1

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.

1. **Coefficients**:
- The coefficients are 2 and 4.
- The GCF of 2 and 4 is 2.

2. **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 **\(2x^2\)**.