Question
greatest common factor of 4x^2y^5 + 10x^3y^4
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GPT-4o mini
To find the greatest common factor (GCF) of the expression \(4x^2y^5 + 10x^3y^4\), we can start by identifying the GCF of the coefficients and the variables.
1. **Coefficients**:
- The coefficients are 4 and 10.
- The GCF of 4 and 10 is 2.
2. **Variables**:
- For \(x^2\) and \(x^3\), the GCF is \(x^2\) (the lowest power of \(x\)).
- For \(y^5\) and \(y^4\), the GCF is \(y^4\) (the lowest power of \(y\)).
Now, combine the GCF of the coefficients and the variables:
\[
\text{GCF} = 2 \cdot x^2 \cdot y^4 = 2x^2y^4
\]
Therefore, the greatest common factor of \(4x^2y^5 + 10x^3y^4\) is \(2x^2y^4\).
1. **Coefficients**:
- The coefficients are 4 and 10.
- The GCF of 4 and 10 is 2.
2. **Variables**:
- For \(x^2\) and \(x^3\), the GCF is \(x^2\) (the lowest power of \(x\)).
- For \(y^5\) and \(y^4\), the GCF is \(y^4\) (the lowest power of \(y\)).
Now, combine the GCF of the coefficients and the variables:
\[
\text{GCF} = 2 \cdot x^2 \cdot y^4 = 2x^2y^4
\]
Therefore, the greatest common factor of \(4x^2y^5 + 10x^3y^4\) is \(2x^2y^4\).
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