factor

Question

9a^2b^3+15a^5b^4

Answer 1

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:

\[ \boxed{3a^2b^3(3 + 5a^3b)} \]