Question

greatest common factor
4a3b-8a2b2+2ab3

Answer 1

To find the greatest common factor (GCF) of the expression \(4a^3b - 8a^2b^2 + 2ab^3\), we can follow these steps:

1. **Identify the coefficients**: The coefficients of the terms are 4, -8, and 2. The GCF of these numbers is 2.

2. **Identify the variable parts**: The variables in each term are \(a\) and \(b\).
- For \(a\), the powers are \(a^3\), \(a^2\), and \(a\). The lowest power is \(a\).
- For \(b\), the powers are \(b\), \(b^2\), and \(b^3\). The lowest power here is \(b\).

3. **Combine the GCF of the coefficients and the variables**:
- The GCF of the coefficients is 2.
- The lowest power of \(a\) is \(a\) and for \(b\) is \(b\).

Thus, the GCF of the entire expression is:

\[
2ab
\]

Now we can factor \(2ab\) out of the original expression:

\[
4a^3b - 8a^2b^2 + 2ab^3 = 2ab(2a^2 - 4ab + b^2)
\]

So, the expression factored out is:

\[
2ab(2a^2 - 4ab + b^2)
\]