Question

What is the greatest common factor of 20x6y+40x4y2−10x5y5?



Responses

10x4y
10 x begin power 4 end power y

20x6y
20 x begin power 6 end power y

5x2y5
5 x squared y begin power 5 end power

5x4y

Answer 1

To find the greatest common factor (GCF) of the expression \(20x^6y + 40x^4y^2 - 10x^5y^5\), we can follow these steps:

1. **Identify the coefficients**:
- The coefficients are 20, 40, and -10.
- The GCF of 20, 40, and 10 is 10.

2. **Identify the variables**:
- For \(x\), we have \(x^6\), \(x^4\), and \(x^5\). The lowest power is \(x^4\).
- For \(y\), we have \(y^1\), \(y^2\), and \(y^5\). The lowest power is \(y^1\) or just \(y\).

3. **Combine the GCF findings**:
- The GCF of the coefficients is 10.
- The GCF for \(x\) is \(x^4\).
- The GCF for \(y\) is \(y\).

Putting all of these together, the GCF of the entire expression is:

\[
10x^4y
\]

Thus, the greatest common factor of \(20x^6y + 40x^4y^2 - 10x^5y^5\) is \(10x^4y\).

The correct response is:
**10 x begin power 4 end power y**