Question

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

2xy
2 x y

4x2
4 x squared

2x2y
2 x squared y

2x2

Answer 1

To find the greatest common factor (GCF) of the expressions \(2x^2\) and \(4x^2y\), we can start by examining the factors of each term:

1. **Factors of \(2x^2\)**:
- This can be expressed as \(2 \cdot x^2\).

2. **Factors of \(4x^2y\)**:
- This can be expressed as \(4 \cdot x^2 \cdot y\).

Next, we can identify the common factors:
- The coefficients are \(2\) and \(4\), and their GCF is \(2\).
- The variable \(x^2\) is common in both terms.
- The variable \(y\) is not present in \(2x^2\).

Now, combining the GCF of the coefficients and the common variables:
- The GCF is \(2 \cdot x^2\).

Thus, the greatest common factor of \(2x^2\) and \(4x^2y\) is:

\[
2x^2
\]

Therefore, the correct response is:

**2x²**.