Question
When factoring the expression:
4x^2y^5 + 10x^3y^4
A. 4xy
B. 14x^5y^9
C. 2x^2y^4
D. 10x^3y^5
4x^2y^5 + 10x^3y^4
A. 4xy
B. 14x^5y^9
C. 2x^2y^4
D. 10x^3y^5
Answers
GPT-4o mini
To factor the expression \(4x^2y^5 + 10x^3y^4\), we need to find the greatest common factor (GCF) of the two terms.
1. **Identify coefficients**: The coefficients are 4 and 10. The GCF of 4 and 10 is 2.
2. **Identify the variables and their powers**:
- For \(x^2\) and \(x^3\), the lowest power of \(x\) is \(x^2\).
- For \(y^5\) and \(y^4\), the lowest power of \(y\) is \(y^4\).
From this, we find the GCF of the entire expression:
- GCF: \(2x^2y^4\)
Now we factor out this GCF from the original expression:
\[
4x^2y^5 + 10x^3y^4 = 2x^2y^4(2y + 5x)
\]
Thus, the correctly factored form highlights \(2x^2y^4\) as the common factor.
Among the provided options, the answer is:
**C. 2x^2y^4**.
1. **Identify coefficients**: The coefficients are 4 and 10. The GCF of 4 and 10 is 2.
2. **Identify the variables and their powers**:
- For \(x^2\) and \(x^3\), the lowest power of \(x\) is \(x^2\).
- For \(y^5\) and \(y^4\), the lowest power of \(y\) is \(y^4\).
From this, we find the GCF of the entire expression:
- GCF: \(2x^2y^4\)
Now we factor out this GCF from the original expression:
\[
4x^2y^5 + 10x^3y^4 = 2x^2y^4(2y + 5x)
\]
Thus, the correctly factored form highlights \(2x^2y^4\) as the common factor.
Among the provided options, the answer is:
**C. 2x^2y^4**.