factor

Question

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

Answer 1

To factor the expression \(9a^{b^3} + 15a^5b^4\), we first look for common factors in the two terms.

1. Identify common factors:

   • The coefficients \(9\) and \(15\) have a greatest common divisor (GCD) of \(3\).
   • For the \(a\) terms, the lowest power is \(a^{b^3}\).
   • There are no common factors with the \(b\) terms since they are different powers of \(b\).

2. Factor out the GCD: We can factor out \(3a^{b^3}\) from both terms: \[ 9a^{b^3} + 15a^5b^4 = 3a^{b^3}(3 + 5a^{5-b^3}b^4) \]

3. Expanding and Final Factored Form: Inside the parentheses, we now have \(3 + 5a^{5-b^3}b^4\).

Thus, the completely factored form of the expression is: \[ 3a^{b^3}(3 + 5a^{5-b^3}b^4) \]