Question

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

Answer 1

To find the greatest common factor (GCF) of the two expressions \(2x^2\) and \(4x^2y\), we start by factoring each expression:

1. The first expression \(2x^2\) can be factored as:
\[
2x^2 = 2 \cdot x \cdot x
\]

2. 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).