Question
factor
9a^2b^3+15a^5b^4
9a^2b^3+15a^5b^4
Answers
Answered by
GPT-4o mini
To factor the expression \( 9a^2b^3 + 15a^5b^4 \), we first look for the greatest common factor (GCF) of the two terms.
1. **Identify the coefficients:**
- The coefficients are 9 and 15. The GCF of 9 and 15 is 3.
2. **Identify the variable parts:**
- For \( a^2 \) and \( a^5 \), the GCF is \( a^2 \).
- For \( b^3 \) and \( b^4 \), the GCF is \( b^3 \).
3. **Combine the GCFs:**
- The overall GCF of the expression is \( 3a^2b^3 \).
Now, we factor this out from each term:
\[
9a^2b^3 + 15a^5b^4 = 3a^2b^3(3 + 5a^3b)
\]
Thus, the factored form of the expression is:
\[
\boxed{3a^2b^3(3 + 5a^3b)}
\]
1. **Identify the coefficients:**
- The coefficients are 9 and 15. The GCF of 9 and 15 is 3.
2. **Identify the variable parts:**
- For \( a^2 \) and \( a^5 \), the GCF is \( a^2 \).
- For \( b^3 \) and \( b^4 \), the GCF is \( b^3 \).
3. **Combine the GCFs:**
- The overall GCF of the expression is \( 3a^2b^3 \).
Now, we factor this out from each term:
\[
9a^2b^3 + 15a^5b^4 = 3a^2b^3(3 + 5a^3b)
\]
Thus, the factored form of the expression is:
\[
\boxed{3a^2b^3(3 + 5a^3b)}
\]
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